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Calculus/Questions Answered by Expert Alon Mandes
| Subject | Date Asked |
| Calc | 3/3/2011 |
| Q: A boat is pulled toward a dock by means of a rope wound on a drum that is located 4 ft above the bow ... A: If we set the length of the rope pulled as y , & the distance traveled by the boat as x , then ... | |
| Trignomentric derivative | 3/2/2011 |
| Q: differentiate cos(sinx)((cosx)) ANSWER: { [cos(sin(x))]*[cos(x)] }' = ... A: sorry , correction : { [cos(sin(x))]*[cos(x)] }' = -[sin(x)]*[cos(sin(x))] - [cos²(x)][sin(sin(x))] ... | |
| help | 1/21/2011 |
| Q: A rectanglular shet of metal of perimeter 36cm and dimensions x and y is to be rolled into a ... A: Perimeter of the rectanglular is : 2x+2y . Thus , 2x+2y=36 --> y=18-x . Hiegth of the cylinder , H=y ... | |
| velocity | 1/2/2011 |
| Q: a ball is thrown upward at a velocity of 100ft/s. the distance of the ball from the ground is ... A: The instantaneous velocity is defined as the derivative of f(t). Meaning : V(t)=-32t+100 . Thus, V(1 ... | |
| Solve this derivative problem | 12/12/2010 |
| Q: How to find the partial derivatives? If f(x, y) = 6x^2 + 2e^xy, find the following. (a) ∂^2f ... A: The key is to treat each variable a seperate one . Now, if you meant that f(x,y) is ... | |
| logarithm, Integration by substitution | 12/10/2010 |
| Q: I have a problem which should be fairly simple, but I wind up stuck at an early point. The problem ... A: Let's perform the substitution : t=av . Thus, dt=adv AND when t=a then v=1 , AND where t=ab --> v=b ... | |
| calculus | 11/30/2010 |
| Q: Find the value of x for which the given function is increasing and those values of x for which it is ... A: Let's derive y : y'=2x+2 . Now, we solve : y'=0 , meaning : 2x+2=0 --> x=-1. This point is called ... | |
| Calculus Question. | 11/22/2010 |
| Q: The position function, s(t)=-16t^2+240t+150, is of an object thrown upward from the top of a 150 ... A: To know When will it strike the ground, we must solve s(t)=0 . The 2 solutions are : t1=-0.6 AND ... | |
| differential calculus | 11/21/2010 |
| Q: Find the slope of a line tangent to the curve by=x^2 at the point P(3,9)by finding the limit of the ... A: The slope of a line tangent to a curve f(x) at point x0 is defined as : s=∆y/∆x . where ... | |
| calculus | 10/29/2010 |
| Q: What is the derivative of modulus of x with respect to x? A: f(x)=|x| . Let's write it in different form : | +x if x>0 f(x)=| -x if x<0 | 0 if x=0 ... | |
| Definite Integral | 10/19/2010 |
| Q: Evaluate the given definite integral. a=-1 ; b=1 [(X^2 + 6X -2)]^2 / 9 dx. Give you please all ... A: Lets do the solution elaborated step by step progress : 1st, let's examine the form inside the ... | |
| calculus / limits | 10/18/2010 |
| Q: For what value of m and b is the statement: lim [sqrt(mx+b)-3]/x=1? x->0 Thank you! A: √(mx+b) - 3 [ √(mx+b) - 3 ] [ √(mx+b) + 3 ] ------------ = ... | |
| slope and differentiation | 10/15/2010 |
| Q: find the slope of the tangent line to the graph of the function at a given point. ... A: I didn't understand if the graph g(x) is whether (3/2)x+1 or 3/(2x+1) or [3/(2x)]+1 . So, I will ... | |
| Rates of change when filling different shaped bottles | 10/3/2010 |
| Q: I am confused about how to draw rough graphs of the rates of change of increasing height in a bottle ... A: Ok Sofia, For every bottle we will assume that the volume of the water is growing lineary in time. ... | |
| calculus | 10/3/2010 |
| Q: The line y=3/2X-4 is tangent at X=6 to the graph of the function f. Find f(6) and f'(6). A: 1st of all lets find f at point x=6 : At point x=6 , the two graphs y & f intersect. That means y at ... | |
| Rates of change when filling different shaped bottles | 10/2/2010 |
| Q: I am confused about how to draw rough graphs of the rates of change of increasing height in a bottle ... A: You attached the figures of the bottles. Each shape has diffrent equation to work with. I need to ... | |
| Particle Motion | 10/1/2010 |
| Q: A particle moves along a so that its position at any time t(greater than or equal to) 0 is given by ... A: (a) Displacement=s(5)-s(0)=5^2-3*5+2-[0^2-3*0+2]=25-15=5 meters. (b) Average velocity=Displacement/5 ... | |
| Expanding sphere | 9/27/2010 |
| Q: To be honest, I have received two very different answers to this question, so need a third that ... A: yes there is amistake in calculating the deceleration and for that I apologize ! here's the ... | |
| can u help me find the answer for this questions? | 9/26/2010 |
| Q: Find the point on the curve r(t) = (5 sin t)ı + (5 cos t) + 12tk at a distance ... A: Ok Farah , let's review our facts : 1. Our trajectory is r(t#=[5Sin#t#,5Cos#t#,12t] Or in other ... | |
| calculus | 9/25/2010 |
| Q: Let f(x) = x+1 and g(x) = -(1/5)x +3 How can we find the size of angles formed by these two lines A: We know that : y1(x)=x+1 y2(x)=3-(x/5) I attached a drawing to illustrate the problem . From the ... | |
| Exonential differentiation | 9/20/2010 |
| Q: What are the first and second derivatives of this sigmoidal equation) y = a + (b/(1 + e^x)) A: b y = a + ----------- 1 + e^x be^x y' = 0 - ... | |
| pyramidal tank | 8/28/2010 |
| Q: The pyramidal tank has a square base of 11.6ft on a side and an altitude of 14.8ft. How many gallons ... A: Let's set d to be the height of level of water from the base . We know that d=5.725 ft . From this ... | |
| Calculus Books | 8/23/2010 |
| Q: I am an undergrad. physics student. I have a bunch of calculus books and they are quite distinct ... A: I myself would rather prefer the pure mathematical approach, for which you will master the art of ... | |
| Trigonometric equation | 8/19/2010 |
| Q: Can u show me how to solve these equations. 1.)tan3x=1 2.) cosx+sinxtanx=2 and 3.)cos2x+sinx=0. If ... A: 1) tan(3x)=1 --> 3x=π/4 --> x=π/12 . 2) cos(x)+sin(x)tan(x)=2 --> ... | |
| calculus | 8/12/2010 |
| Q: Find the center of mass of a thin plate cpvering the given region with the given density function. ... A: We have 2 curves : y=4/x & y=0 . To calculate the C.M , we will 1st calculate : 1. The Mass of the ... | |
| Summation | 7/8/2010 |
| Q: please help me. Thank you. These is a question about summation. Thank you. ... A: (a) x3+x4+X5+x6 = 6 ∑ xi i=3 (b) 5 ∑ x(i)y(ii) = ... | |
| calculus | 7/1/2010 |
| Q: Pick a point c such that the limit of f(x) as x approaches c from the right and the left are equal, ... A: The function that you suggested is f(x)=(x²-c²)/(x-c) . We can see that x=c is a singularity point ... | |
| 4 part question on integration and differential equations i am struggling with | 6/30/2010 |
| Q: given ∫ (f(x))^n f'(x)dx = 1/n+1(f(x))^n+1 +c (n does not = -1)? 1. Using the above equation ... A: 1. Let's consider the integral : ∫ [ (cosx) / √(4-sinx) ]dx . We set f(x)=4-sinx , we ... | |
| DT signals confusion, searched a lot but no perfect answer | 6/27/2010 |
| Q: Q1)determine which of them are periodic and find fundamental period. a) cos ( (PI*30n)/105 ) b) ... A: In section (a) what you did was right . The period is 7 . In section (b) the signal is composed of 3 ... | |
| Calculus | 6/16/2010 |
| Q: Can you please bring me through the steps to solve the problem: Find the value of k that gives ... A: Let's attack this problem from different angle : The function f(x#=kx^2-4x+6 describes a parabola ... | |
| Maths parametric equations | 6/9/2010 |
| Q: got a question show that x=cos2x, y=sinxcosx is equal to x^2+4y^2=1 A: x²=Cos²(2β) ... | |
| Calculus | 6/4/2010 |
| Q: Can you please bring me through the steps to solve the problem: Find the value of k that gives ... A: Let's solve it step by step : first of all , let's calculate f(-2) : f(x)=kx^2-4x+6 , thus ... | |
| Inverse of a function | 5/25/2010 |
| Q: Find a formula for the inverse of the function: f(x)=(6)^(6)^x f-1(x)= ?? A: Ok, we know that : y=6^6^x . Let's find x as function of y : To do so, we perform Log{base 6} for ... | |
| Graph: Sinusoidally | 5/24/2010 |
| Q: A population of animals oscillates sinusoidally between a low of 100 on January 1 and a high of 1200 ... A: The general form of a sinusoidal relation is given by y(t)=A+B*Sin(C*t+D) . All we need to do is to ... | |
| Please try to get me the answer for this question! | 5/22/2010 |
| Q: Evaluate ∫_2^3▒〖e^√(x-2)/(2√(x-2)) dx〗 A: Integral from the form ∫f'(x)*e^[f(x)] dx is always equal e^[f(x)] . This is true because : ... | |
| Limits of a confusing function. | 5/19/2010 |
| Q: On my calculus final I had to take a limit for [cos(x) / abs(x)] as x approaches zero. I thought the ... A: 1st of all l'Hôpital's rule can be applied only on form such as INF/INF or 0/0 . In our case we have ... | |
| derivative | 5/13/2010 |
| Q: find the derivative with respect to x:- under root (a^2cos^2x + b^2sin^2x) NOTE- the equation is ... A: y=√[a²Cos²(x)+b²Sin²(x)] y'={ -2a²Cos(x)Sin(x)+2b²Sin(x)Cos(x) } / { ... | |
| Integration Calculus: Area | 5/7/2010 |
| Q: Area: Find the area of the largest rectangle that can be inscribed under the curve y=e^(-x^2) in the ... A: A(x)=2x[e^(-x^2)] to find max , we derive with respect to x : A'(x)=2[e^(-x^2)]+2x[-2xe^(-x^2)] . I ... | |
| calculus | 5/4/2010 |
| Q: show that the volume of a pyramid of height h whose base is an equilateral triangle of side S is ... A: Let's use infinitesimal approach : The pyramid height increase form h=0->H . At a given height h , ... | |
| double integral | 5/3/2010 |
| Q: Let R1 denote the rectangle [0, 5] × [–4, 4], R2 the rectangle [0, 5] × [0, 4], and R3 the rectangle ... A: ∫∫ f(x,y)dA = ∫∫ f(x,y)dA + ∫∫ f(x,y)dA = ∫∫ ... | |
| stokes' theorem | 4/24/2010 |
| Q: regarding the answer you posted for stokes' theorem. Applying Stokes' Theorem, evaluate the ... A: Sorry, my mistake . -4∫∫(x+y+z) dxdy = -4∫∫ (3a/2)dxdy = ... | |
| stokes' theorem | 4/24/2010 |
| Q: regarding the answer you posted for stokes' theorem. Applying Stokes' Theorem, evaluate the ... A: OK , -2∫∫[y+z,x+z,x+y]•[1,1,1] dxdy = -2∫∫y+z+x+z+x+z dxdy = ... | |
| optimization/max & min | 4/19/2010 |
| Q: Show that the retangle with maximum area for a given perimeter is a square. (This was the earliest ... A: Suppose we have a wire with length p . We can make a lot of geometrical shapes . Let's assume that ... | |
| what are the two equations? | 4/17/2010 |
| Q: A small business uses a minivan to make deliveries. The cost per hour for fuel is F=v^2/360, where v ... A: the Total coast is compound of : fuel coast (per hour) + driver coast (per hour) . The distance is ... | |
| calculus - optimization | 4/11/2010 |
| Q: a cylinder, open at one end and having a surface area of 243п cm^2 is to be made from sheet ... A: The surface area of a cylinder is 2πr²+2πrh . In our case it will be S=πr²+2πrh ... | |
| Calculus | 4/9/2010 |
| Q: Triangle abc is an equilateral triangle with side length 4 feet. Determine the dimensions of the ... A: I attached an image that illustrate the problem. The equation of the line L is : y=4-x . The line L ... | |
| optimization | 3/28/2010 |
| Q: A piece of wire 12 m long is cut into two pieces. One piece is bent into a square and the other is ... A: One piece will be with length x, & the other length is y=12-x . The square : x=4L --> L=x/4 . Area ... | |
| Algebra help? Dont understand how to solve the problems? | 3/20/2010 |
| Q: Please help! 1. Determine the range for: f(x) = 4(x - 3)^2 - 2 a)R = {y ≥ -2} b)R = {y ... A: 1. f(x) = 4(x - 3)^2 - 2 This function have a Domain of : all x The Range is : y ≥ -2 . ... | |
| implicit differentiation | 3/18/2010 |
| Q: If, sin(xy)=x, then dy/dx= A: 1st of let's review some facts regarding implicit derivation : 1. If y=f(x) then d/dx { f(x) } = ... | |
| Calc | 3/10/2010 |
| Q: Use implicit differentiation to find the slope of the tangent line to the curve at the point ... A: The slope of the tangent line is defined as m=y' at point (-4,1) . to derive our implicit curve, we ... | |
| limits and derivates | 3/9/2010 |
| Q: A subatomic particle is traveling in a linear accelerator between time 0 nanoseconds and time pi\pi ... A: In this section we will use the same drill as we did before . a) s'(t)=2cos(t)-2sin(2t). Solving ... | |
| limits and differentals | 3/8/2010 |
| Q: A subatomic particle is traveling in a linear accelerator between time 0 nanoseconds and time 10 ... A: Yes Lynn , sorry , there is a mistake : The solution of s'(t)=0 is : a) 2t^2-10t+11=-2t+5 --> ... | |
| limits and differentals | 3/8/2010 |
| Q: A subatomic particle is traveling in a linear accelerator between time 0 nanoseconds and time 10 ... A: a) The particle at rest when the velocity is zero, meaning s'(t)=0 : ... | |
| derivatives and limits | 3/1/2010 |
| Q: part(a):differentiate f(x) = sec^3x part(b): differentiate: f(x)=(4-x^2)^10 part(c): find ... A: 1. f(x) = sec^3x We know that [sec(x)]'=sec(x)tan(x) . Therefore : f'(x)=3sec(x)tan(x) 2. ... | |
| where is the error? | 2/28/2010 |
| Q: integral (9-x^2)^1/2 * (x-3)^2 dx (3-x)^(1/2) *(x+3)^(1/2) *(x-3)^2 dx (3-x)^5/2 (3+x) dx u = 3-x ... A: (3-x)^(1/2) *(x+3)^(1/2) *(x-3)^2 dx (3-x)^5/2 (3+x) dx <--------- here is the problem . It should ... | |
| Calculus 1 | 2/26/2010 |
| Q: Find the equation of the tangent line to the graph of f(x)=x^2/3 that is parallel to the line ... A: That's right, the slope of the tangent line is m=2x/3 . we need to know x in order to get the slope ... | |
| succesive differenciation | 2/22/2010 |
| Q: y=e^ax sin bx prove that y2-2ay1+(a^2+b^2)y=0 A: y=[e^(ax)][sin(bx)] Let's differentate : y'=[e^(ax)]'[sin(bx)]+[e^(ax)][sin(bx)]' ... | |
| limits and derivates | 2/21/2010 |
| Q: part(a): given that: f(x)= h(x)x^5 h(-1)= 4 h'(-1)= 7 find f'(-1) part(b): differentiate the ... A: part(a): We use the rule : [fg]'=f'g+fg' . Therefore, f(x)= h(x)*x^5 f'(x)=h'(x)*x^5+h(x)*5x^4 ... | |
| Binomial series and taylor series expansion | 2/16/2010 |
| Q: How do you go about finding the Taylor series expansion of x^2/(1+x^2) using the binomial expansion ... A: We know that : 1 + 1/x + 1/x^2 + 1/x^3 + 1/x^4 + .... = 1/(1-x) we also know that : 1 - 1/x + 1/x^2 ... | |
| Calculus II | 2/15/2010 |
| Q: What is the volume of the solid obtained? A region R is bounded by y=0, y=f(x)>0, x=o, x=t>0. If R ... A: Volume of revolution is given by : t 1. V=∫ π y²(x)dx if revolved around the X-axis ... | |
| calculus AB | 2/12/2010 |
| Q: my teacher just went on maternity leave as she left us with a set of questions, this is one of them ... A: As we know, if x(t) is the function expressing the position of a particle, then : 1. ... | |
| Help | 2/9/2010 |
| Q: F(x)=sin(pie * x)/ x squared - 1 This is the problem. I have found its discontinuities, but I don't ... A: Im sorry I didn't understand the form of the function . Whether its : sin(πx) ------- x ... | |
| Finding antiderivative | 2/7/2010 |
| Q: can u help me find the antiderivative of this: (sec²x)/(4-tan²x)^3/2 dx A: The derivative of f/g^(3/2) is : f'*g^(3/2)-f*(3/2)*g'*g^(1/2) ------------------------- . ... | |
| optimization | 2/1/2010 |
| Q: A window consisting of a rectangle topped by a semi circle is to have an outer perimeter P. Find the ... A: I attached an image or a drawing to illustrate the problem . P=2x+2y+2πr . Since r=y/2 , then ... | |
| a calculus two question | 1/31/2010 |
| Q: consider s=f(t)= sin t on {0, 2 TT--that is suppose to be the symbol for pi---0, 2 PI). How far ... A: S(t) represents the distance of the particle from the origin . at 0<t<pi/2 the particle is moving ... | |
| Related Rates | 1/26/2010 |
| Q: I am in desperate need of help with this problem: A pyramidal watering trough is being filled at a ... A: I attached an image to illustrate the figure . From geometry , we know that : h/3=x/10 therefore : ... | |
| limits | 1/24/2010 |
| Q: lim 7^3-3^2+x (2) lim 2x^4-3x (3) lim x-15 xto infinity x to infinity x to ... A: Let's solve it step by step : 7x^3-3x^2+x Lim ------------ = ? x->∞ ... | |
| applications of absolute extrema | 1/17/2010 |
| Q: good day, sir! i'm doing some practice problems for my calculus exam, and i saw thisA cardboard ... A: If we set the dimensions of the cardboard as : AxB , then The area of the printed region is : S=[A- ... | |
| integrals. | 1/14/2010 |
| Q: My question is: 1. Use the midpoint rule to approximate the integral. *integral sign [7,16] ... A: According to midpoint rule : b ∫ f(x) dx = ∆x[f(x1)+f(x2)+...f(xn)] where ... | |
| integral problem | 1/12/2010 |
| Q: the question asks to calculate the integral of x^2/(x^2+1)^2 dx thanks A: 1st of all , let's pay attention for 2 major things : 1. { Arctan(x) }' = 1/(1+x^2) 2. { x/(1+x^2) ... | |
| L'Hospital | 1/11/2010 |
| Q: i've got : 1) Lim(x-Lnx) as x approaches infinity !! we should use the L.hospital Rule but it is ( ... A: 1) the function f(x)=x-ln(x) is rapidly increasing . Because always ln(x)<x , and when x is very ... | |
| bunch of Qz involving limitz | 1/9/2010 |
| Q: 1)is Lim e^(x-x^2) as x approaches infinity =0 ???? 2)just to make sure, there is no vertical ... A: 1) Lim e^(x-x^2) = 0 ("because x-x^2 is negative for all x>1") x->INF 2) y=(square root ... | |
| largest inscribed triangle | 1/1/2010 |
| Q: Points A and B lie at the ends of a diameter of a unit circle and point C lies on the ... A: The angle ACB is 90 degrees . The sides of the right triangle are : AB=d (Diameter) AC=y BC=x ... | |
| Calculus AP | 12/31/2009 |
| Q: Find the intervals of increase or decrease, local max and min, concavity and points of inflection. ... A: y=x/(x^2-9) y'=[x^2-9-x(2x)]/(x^2-9)^2 y'=0 : x^2-9-2x^2=0 --> x^2+9=0 . No solution in the real ... | |
| critical number & extreme values | 12/29/2009 |
| Q: can you please help me with those : find the critical numbers for : h(t)=t^(3/4)-2t^(1/4) ... A: Yes. Sorry, my mistake , I apologize. 1. (2/5)x-(8/5)+x=0 --> x=8/7 . yes 2. sin(t)=cos(2t) --> We ... | |
| calculus problem | 12/28/2009 |
| Q: The problem gives two functions with variables. We are supposed to compare the equations and then ... A: Our piecewise function is : | e^(ax) , x<=1 f(x)=| | b+Ln(x) , x<1 In order for f(x) to ... | |
| critical number & extreme values | 12/28/2009 |
| Q: can you please help me with those : find the critical numbers for : h(t)=t^(3/4)-2t^(1/4) ... A: h(t)=t^(3/4)-2t^(1/4) h'(t)=(3/4)t^(-1/4)-(1/2)t^(-3/4) h'(t)=0 --> (3/4)t^(-1/4)=(1/2)t^(-3/4) --> ... | |
| Hopital | 12/23/2009 |
| Q: What is Hopital? A: H'lopital rule gives a tool to make it more easy to find & calculate limits, specially if the ... | |
| derivative | 12/20/2009 |
| Q: I've been staring at this problem for a very long time. I know that I have to use chain and product ... A: f(x)=[(4x)^(1/2)]*[(6x+2)^4]=[2x^(1/2)][(6x+2)^4] ... | |
| differentiation | 12/18/2009 |
| Q: I need help differentiating the following function please. f(x)=(sqrt ... A: I think you meant "Ln" when you wrote "In" . ... | |
| application of integration problem | 12/15/2009 |
| Q: Good evening! I'm stuck on this problem.. I hope you can explain it step by step for me. :) Find b ... A: I attached a drawing to illustrate the problem . From the drawing we can easily see that : ... | |
| integrations | 12/13/2009 |
| Q: ok ...i seem to be having a problem sending you the questions so may be i can word it correctly. ... A: f(x)=cos[x]/(1-cos[x]^2)=cos[x]/sin[x]^2 . ("cosx[x]^2+sin[x]^2=1") . Note that (sin[x])'=cos[x] & ... | |
| Limit Laws | 12/11/2009 |
| Q: I have difficulty understanding the formal proofs to the Limit of Sum Law and Limit of ... A: As I mentioned above , the definition of the term : Lim f(x) = L is : ... | |
| Limit Laws | 12/10/2009 |
| Q: I have difficulty understanding the formal proofs to the Limit of Sum Law and Limit of ... A: The definition of Lim f(x) = L x->a Given any real %26 small number ε>0 , there exists ... | |
| Integration by parts | 12/9/2009 |
| Q: I need to find the integral of 3e^(5x)* sin(2x) dx. I have been having a lot of trouble with ... A: In this question we will use the Integration by parts twice in cycle way . Let's do it : We take ... | |
| Integration by parts | 12/9/2009 |
| Q: I need to find the integral of (2x^2 + 5)*e^(2x)dx. I've been having a lot of trouble with the u and ... A: ∫(2x^2+5)*e^(2x)dx=5∫e^(2x)dx+2∫(x^2)e^(2x)dx=(5/2)e^(2x)+2∫(x^2)e^(2x)dx . ... | |
| Calculus Limits | 12/7/2009 |
| Q: A dynamite blast blows a heavy rock straight up with a launch velocity of 160 ft/sec. It reaches a ... A: s(t)=160t-16t^2 is the height as function of time . The velocity as function of time is s'(t): ... | |
| Last question | 12/7/2009 |
| Q: This one I feel like I'm getting right but i'd like to verify with your answer. A ladder is ... A: Let's set v to be the velocity or rate of change in the ladder bottom. Ho is the initial height of ... | |
| Calculus Help! Abs Max and Abs Min | 12/6/2009 |
| Q: Find the absolute maximum and absolute minimum for the function on the indicated interval. ... A: 1st step , let's chick the edges : f(0)=21. f(6)=9 . Now, let's derive & solve f'=0 : f'(x)=2x-8 ... | |
| linear approximation | 12/4/2009 |
| Q: Q)use linear approximation to estimate tan(44) ? i started with : f(x)= tan(x) f(45)=1 ... A: f(x)=tang(x) L(x)=f(xo)+f'(xo)(x-xo) In our case , xo=45 , x=1 . Therefore : ... | |
| please, help needed for today | 12/3/2009 |
| Q: Suppose a particle is observed moving along a straight line, and suppose that the velocity v of ... A: v(t)=2sin(pit) The particle is at rest when v(t)=0. Therefore : sin(pit)=0 --> t=0+k*pi --> t=pi . ... | |
| Applied max and min | 12/3/2009 |
| Q: A closed cylindrical canister or volume 8(pi) cubit feet is to be made. It must stand between two ... A: The volume of the canister V=πr²h & it's equals 8π . Therefore r²h=8 --> h=8/r². The total ... | |
| Looking for relative minima, maxima and extrema | 11/30/2009 |
| Q: Graph the fourth-degree polynomial p(x)=x^4+ax^2+1 for various values of the constant a. a)Determine ... A: p(x)=x^4+ax^2+1 p'(x)=4x^3+2ax p'(x)=0 : 2x^3+a=0 -- > xo=-(a/2)^(1/3) . We can see that we can have ... | |
| calculus | 11/30/2009 |
| Q: show that the volume of a sphere is 4/3π(r^3) using a volume of revolution calculation. A: If we take a an upper side of a circle, it has the equation of y=√(r²-x²). That's true because ... | |
| calculus | 11/30/2009 |
| Q: find the volume generated by rotating the region bounded by y=(x^4), y=0 and x=1 about the line x=2. A: The volume is : b 2π∫Radius*Height dx . In our case : Raduis=2-x , & Height=f(x0. ... | |
| BC Calculus Optimization & Differentials Problem | 11/30/2009 |
| Q: What is the area of the largest rectangle that can be inscribed under the curve where x is in the ... A: If we assume that the curve has a function : y=f(x) , where f(-pi/2)=f(pi/2) then, S(x)=2x*f(x) . to ... | |
| Calculus derivative | 11/29/2009 |
| Q: We are on differentiation and derivative. This question is very confusing. I hope someone can help ... A: The tangent line has an equation from the form : y=mx+n . Let's find m & n : m is the slope = f'(x) ... | |
| Calculus | 11/29/2009 |
| Q: Here is myGiven the graph below, please sketch the f'(x) and f''(x). Hint: try and figure out what ... A: 1. From the graph we can see that the roots of the polynom or the point of intersect with the ... | |
| Calculus | 11/29/2009 |
| Q: Here is myGiven the graph below, please sketch the f'(x) and f''(x). Hint: try and figure out what ... A: Every polynom f(x)=ax^3+bx^2+cx+d will have derivatives as follow : f'(x)=3ax^2+2bx+c f''(x)=6ax+2b ... | |
| derivatives :( | 11/28/2009 |
| Q: what is the derivative of e^-x? & What is the derivative of e^(4ln(x^3))? A: The derivative of e^[f(x)] is f'(x)e^[f(x)] . Therefore : [e^(-x)]'=-e^(-x) . ... | |
| Calculus | 11/28/2009 |
| Q: please help! You need to build a tin can (including the top and bottom) with a volume of 500 cubic ... A: The dimensions of the can are : 1. radius of top %26 bottom = r 2. height = h Therefore the amount ... | |
| Gradients | 11/27/2009 |
| Q: My name is Vincent and I'm currently a high school student. I'm having a little trouble understand a ... A: The gradient of a function is the derivative of the function with respect to a given variable. The ... | |
| Limits | 11/24/2009 |
| Q: Do you know where can I find a web with limit problems focusing on radicals in undetermined forms? ... A: (x^2+4x+7)^(1/2) (x^2+4x+7)^(1/2) 1/x Lim ------------------- = ... | |
| Applied Max/Min Problem | 11/24/2009 |
| Q: I have started this question but am not sure if I am doing it correctly. Your help will be greatly ... A: 2x+5y=70 --> x=(70-5y)/2 we want to maximize x*y : x*y=(70-5y)y/2=(70y/2)-5y^2/2=35y-2.5y^2 To find ... | |
| Velocity, acceleration and curvature | 11/24/2009 |
| Q: I know that for the first question i need to find the derivative and then the double derivative, but ... A: R(t)=2t[i] + 3t^2[j] + sin(t)e^(-t)[k] Velocity=V(t)=dR/dt=R'(t)=2[i]+6t[j]+ { ... | |
| Critical Numbers | 11/19/2009 |
| Q: Find critical numbers and relative maximum(s), and relative minimum(s) of f(x)=x^4-6x^2+2 A: f(x)=x^4-6x^2+2 f'(x)=4x^3-12x f'(x)=0 : 4x^3-12x=0 --> x(4x^2-12)=0 . Solutions : x1=0, ... | |
| calcus | 11/13/2009 |
| Q: find a point on the graph of y=e 5x at which the tangent line passes through the origin A: Tangent line that passes through the origin will have the equation : y=mx . Where m is the slope of ... | |
| calculus 1 | 11/13/2009 |
| Q: A boat leaves the dock at 2 pm. and travels due south at a speed of 20mph. Another boat, which had ... A: Let's set this time as to . After 1 hour boat B arrived to the dock. That means that at 2pm after to ... | |
| Calculus | 11/13/2009 |
| Q: Find the equation of the tangent line to the following curves at the given point 1. y= 1/cube ... A: In order to find the equation of the tangent line y=mx+n . Where m is the slope & n is the intersect ... | |
| the derivative of y=sinx and y=cosx | 11/12/2009 |
| Q: An isosceles triangle is inscribed in a circle of radius R. Find the value of angle theta that ... A: I attached a drawing of the circle & the triangle with all the angles . Area=S=½X²Sin(Ө). ... | |
| advanced calc question | 11/12/2009 |
| Q: Suppose that the function f is continuous on [a,b], x1 and x2 are in [a,b] and k1 and k2 are ... A: No, No M.V.T is needed. %26 besides M.V.T concerns the derivative , so it's irrelevant. What we ... | |
| Calculus | 11/12/2009 |
| Q: Find the slope of the tangent line to the folowing curves at the given value of x: y=(x^2-2x+2)^5 ... A: The slope of the tangent line is simply the value of the derivative at that point. Say, ... | |
| Differentiation | 11/12/2009 |
| Q: 1)A firm's demand curve for a product is given as P=300-25Q a. What in you view is the total revenue ... A: If we have a function that is polynom such as : f(x)=ax²+bx+c then the derivative will be : ... | |
| successive derivaties | 11/12/2009 |
| Q: find d^y/dx^2 for the following functions 1) xy+2y=5x 2)x^2+y^2+a^2 3)x^3+y^3= a^3 A: 1) d/dx { xy+2y } = d/dx {5x} y+xy'+2yy'=5 y+y'(x+2y)=5 y'=(5-y)/(x+2y) d/dx { y+xy'+2yy' } = d/dx ... | |
| Derivative of Exponential Function | 11/11/2009 |
| Q: I need the derivative of the following cumlative distrubution function with respect to x. f(x) = ... A: A-Ae^(-8Bx) f(x)= ------------------ 1+Ce^(-8Bx) IF y=[f/g] then ... | |
| Differentiation | 11/11/2009 |
| Q: 1)A firm's demand curve for a product is given as P=300-25Q a. What in you view is the total revenue ... A: 1) Is out of my expertise . 2) f(x) = (1/3)x^3 + (5/2)x^2 - 14x + 5 . Let's derive & solve f'=0 : ... | |
| Derivative of Exponential Function | 11/11/2009 |
| Q: I need the derivative of the following cumlative distrubution function with respect to x. f(x) = ... A: A*(1-e^-8Bx) A-Ae^(-8Bx) f(x)= ------------------ = --------------- ... | |
| Word problem | 11/11/2009 |
| Q: I've tried to figure this one out but I keep getting stuck, help please. Q. A farmer plans to fence ... A: Let's set x to be the length of the rectangle of the fence %26 y is the width . Thus, xy=180000 --> ... | |
| Diff. of Log | 11/10/2009 |
| Q: Hey I'm not even sure how to attempt this problem without the denominator being zero. Use the ... A: Here we simply can perform the trick by switching h instead of x . It will give the same result : ... | |
| complex number | 11/10/2009 |
| Q: I keep having trouble understanding in complex number solving.And i am hopping you could show me how ... A: every complex number z can be represented by either on of two: Cartesian Rep : a+jb or simply ... | |
| Optimization Problem #4 | 11/9/2009 |
| Q: Any chance you could look at another optimization problem? I tried to attach the PDF document but ... A: sorry, The v(x) should be : V(x)=144x-54x²+4x³ . So, v'(x)=144-108x+12x² . v'(x)=0 : 144-108x+12x²=0 ... | |
| Optimization Problem #4 | 11/8/2009 |
| Q: Any chance you could look at another optimization problem? I tried to attach the PDF document but ... A: Our cardboard has dimensions of : 8X18 . Our function is ... | |
| Proving L'hospital's rule | 11/8/2009 |
| Q: if f'' is continuous show that Lim h->0 f(x + h) -2f(x) + f(x-h) ------------------------ h^2 = ... A: The definition of f'(x) is : Lim{h->0} [f(x+h)-f(x)]/h . Therefore, The definition of f''(x) will ... | |
| complex integral using parametrizatin | 11/8/2009 |
| Q: Using parameterization perform: ∮〖(e^z)dz〗along c:|z|=1 ANSWER: ... A: a) f(z)=e^(3z). Our parametrization will be : z(t)=(1+i)t , where 0≤t≤1 . Therefore : ... | |
| Optimization Problem | 11/7/2009 |
| Q: Can you show me how to work through this problem? THANK YOU! 5. (1 pt) A parcel delivery service ... A: If x is the side of the square and y the length of the box, then : Volume=yx²2 & ... | |
| Calculus | 11/7/2009 |
| Q: Explain why the Mean Value Theorem does not apply to the function f(x)= x to the 1/3 on the interval ... A: The mean value theorem states that f(x) is continuous on the closed interval [-1,1], & ... | |
| Lines tangent to ellipse | 11/5/2009 |
| Q: Find the equations of both tangent lines to the ellipse ((x^2)/4)+((y^2)/9)=1 that pass through the ... A: Let's suppose that the point where the tangent line touch the ellipse is (xo,yo). We can find a ... | |
| precalculus!!! | 11/5/2009 |
| Q: write a 4th degree polynomial with the given zeros 2,-2-5i A: 4th degree polynomial has 4 zeroes. We have been given 2, we need to find the other 2. Since complex ... | |
| Unknown values | 11/5/2009 |
| Q: I'm not sure how to approach this problem. For what values of the numbers A and B does the function ... A: It's given that f(2)=1. Therefore : A(2)e^(B(2)^2)=1 --> 2Ae^(4B)=1 --> A=1/[2e^(4B)] --> ... | |
| calculus | 11/5/2009 |
| Q: A particle moves along the x-axis so that its x-coordinate at time t is given by x=ae^-kt+be^kt. ... A: x(t)=a[e^(-kt)] + b[e^(kt)] is the position function . 1st derivative will gives us the velocity ... | |
| calculus | 11/5/2009 |
| Q: Show that f(x)=|x²-9| is continuous but not differentiable at x=-3 and x=3. Sketch graphs of f' and ... A: Continuosity : ------------ Lim f(x) = Lim f(x) x->3- x->3+ Let's calculate the ... | |
| Pre-Calculus | 11/4/2009 |
| Q: I need help with this problem, please: State an equation whose graph is a transformation of the ... A: The general sine function has a form of : Asin(ωt+Ø) . where : A is the amplitude . ... | |
| calculus 1 extrema of a function | 11/4/2009 |
| Q: locate the absolute extrema of the function y=xLn(x+3) on the interval of [0,3] A: Lets derive y : y'=Ln(x+3) + x/(x+3). y'=0 --> Ln(x+3)=-x/(x+3) . There is no x in the interval ... | |
| tangent lines on a curve | 11/4/2009 |
| Q: Homework help calculus 2 is killing me...this question ask to find the equation of the tangent line ... A: The parametrization of the curve : x=√t & y=1/[2t²] . To find slope of the tangent line, we ... | |
| Pre-Calculus | 11/3/2009 |
| Q: ) Suppose a parabola has focus (1, 7) and directrix y = 3. What is the equation of the parabola? ... A: A parabola can be defined as the set of all points such that the distance from a point on the ... | |
| Integals | 11/3/2009 |
| Q: the question asks to calculate the integral Z=(integral)R (x^2-y^2)dR Where R is the region of a ... A: The region R can be described in polar form as : 1≤ρ≤2 %26 ... | |
| calculus | 11/3/2009 |
| Q: i have a question about a ladder 10ft long rests against a vertical wall. If the bottom of the ... A: According to Pythagoras : sin(θ)=(x+2t)/10 . Where x is the distance between the bottom of the ... | |
| Question | 11/3/2009 |
| Q: Intelligence reports to the U.S. fleet admiral the an enemy task force is located 120 nautical miles ... A: I have attached an image of a diagram that illustrate the vectors. We need to find θ & to . To ... | |
| urgent math | 11/3/2009 |
| Q: Hey there I have a test tomorrow nigh for Calc and I just can't seem to get the answers for these ... A: #Q1 a)Let's set x(t) the distance from the 2nd base . The distance from the 1st base will be 90-22t ... | |
| calculas | 11/2/2009 |
| Q: if f = (1+x)^1/2/(1-x)^1/2 find dy / dx A: (1+x)^(1/2) y= ----------- (1-x)^(1/2) The rule determine : [f/g]'=(f'g-g'f)/(g^2) . ... | |
| Functions | 11/1/2009 |
| Q: Investigate y=lnx/1-lnx.Graphic needed too A: The investigation process of the graph y=Ln(x)/[1-Ln(x)] will be as follow : Step #1 Finding points ... | |
| differntial calculas | 10/31/2009 |
| Q: 3√((4-5x^2 )^4 ) A: I'm sorry sir, but you didn't explain what the question require ... If you meant to know how to ... | |
| Asymptotes polynomial | 10/28/2009 |
| Q: I need to sketch a graph of y=x^4 +4x^3 I need to find the horizontal and vertical asymptotes by ... A: All polynomial functions such as N f(x)=∑ (an)x^n n=1 Are continues %26 have no ... | |
| Pre calc | 10/28/2009 |
| Q: HOw do I solve an equation like this sin X = - cos x A: sinx=-cosx --> snix+cosx=0 . Let's set sinx=t . We know that sin²x+cos²=1 therefore : ... | |
| Calculus | 10/25/2009 |
| Q: How many lines which are tangent to the curve y= x/x+1 pass through the point (1,3)? where do they ... A: Since the function f(x)=x/(x+1) is symmetric along the line y=x+1 , we will get 2 tangent lines from ... | |
| Calculus | 10/25/2009 |
| Q: For what values of x between 0 and 2pi is the function f(x)= x-2sin(x) increasing? A: Function f(x) is increasing when f'(x)>0 . Therefore we will derive f & solve the inequality f'>o : ... | |
| function | 10/25/2009 |
| Q: prove that f(x)-(f-x) is an odd function but f(x)+f(-x) is a an even function of X . Show with ... A: 1st of all we must remember the definition of even %26 odd, %26 here they are : Function h(x) is ... | |
| volume of tetrahedron | 10/24/2009 |
| Q: find the volume of a tetrahedron formed by the plane x+2y+3z=6 and the coordinate planes A: The volume of the tetrahedron is : V=(1/3)*A*h . Where : A is the area of the triangle base, %26 h ... | |
| Calculus Minimize Cost | 10/21/2009 |
| Q: The cost of operating a truck is 250 + .31v cents per mile when the truck runs at a steady speed of ... A: Let's set C to represent the coast of operating the truck. Let's set S to represent the coast to be ... | |
| Extreme Values in Calclus | 10/21/2009 |
| Q: I am taking AP Calculus as a high school senior. First of all, how does this course compare to ... A: f(x)=(1/x)+ln(x) f'(x)=-(1/x²)+(1/x) Extreme values are achieved when f'(x)=0. So, -(1/x²)+(1/x)=0 ... | |
| Chain Rule | 10/20/2009 |
| Q: Let f be a differentiable function. use the chain rule to show that : (a) if f is even then f0 is ... A: Let's 1st of all review the definitions of even & odd : Function f(x) is even if : f(x)=f(-x) ... | |
| Tangent lines in triangle | 10/20/2009 |
| Q: Find the area of the triangle formed by the x-axis, the tangent to the graph of f(x) = 6x-x^2 at the ... A: I have attached a drawing to illustrate the problem. # The Blue Line , is the Tangent line , has ... | |
| Calc 1 | 10/20/2009 |
| Q: I'm having trouble finding the derivative of g(x)= (1+4x)^5(3+x-x^2)^8 and is this problem the ... A: We will follow the rule : [fg]'=f'g+fg'. In our case : f=(1+4x)^5 & g=(3+x-x^2)^8.Therefore, ... | |
| Calculus | 10/16/2009 |
| Q: A particle is moving along a curve y=(1+x^3)^(1/2) As it reaches point (2,3), the y-coordinate is ... A: In this section we will use the derivation simple rule : dy/dt=y'(x)*[dx/dt] . Where dy/dt=4 %26 ... | |
| Calculus Limit Problem | 10/14/2009 |
| Q: I am having trouble figuring out the problem below. I have a decent understanding regarding limits ... A: In this section we will use the simple rule : (a+b)(a-b)=a²-b² . This rule can also be written as : ... | |
| equation of the tangent line through the given point | 10/13/2009 |
| Q: f(x)=x^2-3x+4, at P(2,2) A: The tangent line will be from the form of y=mx+n . We need to calculate m & n . Calculating m : ... | |
| Mtrix question | 10/13/2009 |
| Q: Find the matrix A given ethe equation. please answer me ASAP ... A: Yes, I checked it again %26 I had a mistake in writing the program in Matlab software. The final %26 ... | |
| circle formulae | 10/12/2009 |
| Q: Hey, I'm in first year calculus in university and it seems my prof expects us to know the xy formula ... A: Yes , the circle equation in x-y plane is : x^2+y^2=r^2. Where r is the radius. But, this equation ... | |
| calculus 1 | 10/12/2009 |
| Q: find extremum of the function x-2cosx A: Our function is f(x)=x-2Cos(x) . Let's derive it : f'(x)=1-(-2sin(x))=1+2Sin(x) . To find extremum , ... | |
| Pre Calculus -(Honors Advanced Math II class) -sine and cosin waves | 10/12/2009 |
| Q: Here's some background information for the problem: One day w decide to go to six flags. They ... A: I will solve section B. As for section A, you can see it more clearly through the formula. Yes, the ... | |
| calculas | 10/12/2009 |
| Q: A person 2m tall walks away from a streetlight at the rate of 1m/s. If the light is 6m above ground ... A: I attached a drawing to illustrate the exercise. v is the velocity of travelling, x is the length of ... | |
| Mtrix question | 10/11/2009 |
| Q: Find the matrix A given ethe equation. please answer me ASAP A: Let's review a basic fact concerning Matrix equations : Suppose that A,B %26 C are square matrices, ... | |
| finding second derivatives? | 10/11/2009 |
| Q: Use implicit differentiation to find the second derivative of: 2xy^2=4 (nothing is in parenthesis) ... A: Ok Tiffany, let's review %26 sharpen some of the basic facts concerning implicit derivation : 1st of ... | |
| I gave you the wrong equations on BOTH | 10/11/2009 |
| Q: okay, Alon ... I know you're going to think I'm a complete idiot. But BOTH of the equations I gave ... A: It's ok Felipe , it happens to all of us . The 2nd one I have solved a couple of minutes ago, so I ... | |
| Calculus - Integration Problems | 10/10/2009 |
| Q: 2 questions - struggling for 2 hours now, need help! 1) Integrate: ∫ 3t^2 + 4t + 8 dt In ... A: In general , the rule for polynoms integration is : ∫t^n dt = (1/n+1)t^(n+1) . When the ... | |
| Calculus - Integration Problems | 10/10/2009 |
| Q: 2 questions - struggling for 2 hours now, need help! 1) Integrate: ∫ 3t^2 + 4t + 8 dt In ... A: Ok Felipe, let's do it step by step : Due to the linearity of integration , we can claim that : ... | |
| calculas | 10/10/2009 |
| Q: find the derivative [x+{x+(x)^0.5}^0.5]0.5 A: [x+{x+(x)^0.5}^0.5]^0.5 = √[x+√(x+√x)] . Let's break it to multi functions : ... | |
| calculas | 10/9/2009 |
| Q: gravel is being dumped from a conveyer belt at a rate of 40feet per minute. it forms a pile in the ... A: 1st of all, the volume of the cone is (1/3)πr²h & not (4/3)πr³h. & in our case r=h always, ... | |
| calculus | 10/9/2009 |
| Q: find the derivative by implicit way for sin(xy)=x (show step by step please) Thanks A: 1st of all we need to refresh our memory with some abstracts : 1. The derivative of [f(x)g(x)] is ... | |
| calculas | 10/9/2009 |
| Q: Using the formal ǫ − δ definition of limit, show that if limx!a f(x)=L and limx!a ... A: We know that : Lim f(x) = L . That means : x->a for each real ε1>0 there exists a real ... | |
| calculas | 10/9/2009 |
| Q: Exercise 11. Using the formal ǫ − δ definition of limit, show that if f(x) = c then ... A: The definition of the limit, Lim f(x) = L is : x->a For each real ε > 0 there exists a real ... | |
| calculas | 10/9/2009 |
| Q: Exercise 20. Find different functions y defined on the entire real line whose derivatives are such ... A: Let's now take the function y=Asin(x)+Bcos(x) . This is a sum of two solutions. Let's see if this ... | |
| calculas | 10/9/2009 |
| Q: Exercise 19. Find a function y defined on the entire real line whose derivatives are such that ... A: The 1st thing that pups into our mind is : what function that her second derivative is in an ... | |
| calculus question | 10/9/2009 |
| Q: Im sorry to disturb you but I had a calculus question that I needed a bit of help with. This is ... A: The definition of the arc length is : 1 ∫√[1+f'(x)²] dx . In our case f(x)=6x(1-x), ... | |
| Double Intergrals | 10/8/2009 |
| Q: Alon how are you? I am getting my intergration incorrect with double intergrals the questions ... A: I'm fine thank you. The issue here is to transform to polar coordinates. Because the integral of ... | |
| Line Intergral | 10/6/2009 |
| Q: I am having trouble with the following Find the value of the line intergral (intergral sign)F.dr ... A: 1st of all, we need to write the vector field F in terms of t : out trajectory (path) of integration ... | |
| limit theorems | 10/5/2009 |
| Q: I have been wondering of why the the limit of a polynomial as x approaches something we can ... A: The limit definition doesn't change, whether it's a polynom or a fraction. But the issue of ... | |
| Question | 10/4/2009 |
| Q: Hey=) Sorry to disturb you but I have this really difficult question that I just cant figure out: ... A: Here are 2 functions that satisfy the above : 1. f(x)=6x(1-x) 2. f(x)=(π/2)sin(πx) You ... | |
| Calculus - Derivatives | 10/3/2009 |
| Q: Mandes, I need to find the derivative of f(x) = 1 / (squareroot) of (x+2). I've been working on ... A: In this section we will use the trick : √a-√(a+b)=-b/[√a+√(a+b)]. This is ... | |
| Definite Integrals | 10/2/2009 |
| Q: I am trying to answer my assignment in Calculus. It has been hours but I am still confused. I am ... A: Sorry, my mistake, here's the correct answer : From table of integrals we can notice that ... | |
| Applications of integration... | 10/1/2009 |
| Q: I need to find the volume obtained by rotating the region bounded by the curves y=sqrt(x) and y=x. ... A: 1st of all, let's find the point of intercept of both curves : √x=x --> x=0 & x=1 . That means ... | |
| calculus | 9/29/2009 |
| Q: A sequence of real number (a_n)_n=1(n goes to infinity) converges to a real number l if for every ... A: Let's explain it by an example : Suppose we want to chick the convergence of the sequence a(n)=1/n , ... | |
| limits | 9/28/2009 |
| Q: I'm confused on this question and I have a test tomorrow. The limit x->infinity of (3x^4)*((sinx)/x) ... A: We know that sin(x) is always bounded between -1 & 1 . So our function will become : ... | |
| Calculus 1 | 9/26/2009 |
| Q: I can't figure out how to prove the statement using the epsilon,delta definition of this limit. ... A: 1st let's note that : (X^2+X-12)/(X-3)=(X-3)(X+4)/(X-3)=X+4 . To prove that Lim X+4 = 7 X->3 ... | |
| calculus 1 | 9/22/2009 |
| Q: I'm having trouble finding the domain and range of this problem..Not sure of the steps to take.. ... A: Domain of function f(x) is the set of values allowed, or the set of values in which f(x) is defined ... | |
| Limits of infinity | 9/19/2009 |
| Q: I need help on finding the limit as x goes to infinity of (5/x^3-cos1/x)(3+cos1/x) A: The Limit is -4 . Her's why : Lim (5/x^3-cos1/x)(3+cos1/x) = (5/INF-cos1/INF)(3+cos1/INF) = ... | |
| Calculus hw | 9/17/2009 |
| Q: I need help with two problems. The first is: maximize the utility function f(x)= log(x) over x^4. ... A: In this case, the constrain can be substituted directly to U(x,y). There is no need for "Lagrange ... | |
| calculus | 9/15/2009 |
| Q: How can a domain be both an open and closed region? For example, f(x,y) = 4x^2 + 25y^2. I know the ... A: Your question is reasonable, but you have to keep in mind that Infinity is not a number, or yet is ... | |
| trigonmetry | 9/10/2009 |
| Q: prove that (sinA.sin2A+sin3A.sinA6A)/(sinA.cos2A+sin3A.cos6A)=5tanA ... A: This statement is not correct . It should be : (sinA.sin2A+sin3A.sinA6A)/(sinA.cos2A+sin3A.cos6A)= ... | |
| Tangent Lines | 9/9/2009 |
| Q: I believe this question is more pre-calculus, but I just can't seem to figure out where to even ... A: I will call our tangent line T(x). We will suppose that T(x)=mx+n . & we want to find m & n. 1st, we ... | |
| derivative of equation | 9/9/2009 |
| Q: derivative: sqrt(log3^(x^2-x)) i simplified to sqrt( (x^2-x) * (log3) ) then i used the product ... A: In this case there is no need for the product rule, note that log(3) is a constant . Sqrt[ (x^2-x) * ... | |
| calculus | 9/8/2009 |
| Q: find the limit of the function (3^x-3^-x/3^x+3^-x) as x approaches infinity A: Lim [ 3^(x) - 3^(-x) ]/[ 3^(x) + 3^(-x)] = ? x->∞ Note that : [ 3^(x) - 3^(-x) ]/[ 3^(x) + ... | |
| maximum area of rectangle inscribed in a triangle | 9/6/2009 |
| Q: Give the largest rectangle inscribed in the triangle formed by line y=0. y=x and 3x+y=20 if one side ... A: I attached an image that illustrate the drawing of the rectangle inscribed in the triangle. We know ... | |
| trigonmetry | 9/5/2009 |
| Q: sin(2A)=2sinA cosA =(2sinA cos^2A)/cosA =2tanA/sec^2A =2tanA/1+tan^2A please explain it A: Let's decompose the answer into steps : Step 1 : According to the law of trigonometry : ... | |
| Derivatives | 9/3/2009 |
| Q: Find the derivative of the function f(x) = sqrt(x+1) (e^3) Can you walk me thru this one please? ... A: I think you meant f(x)=[e^3x]*√(x+1) . In this case we will follow the rule : [f*g]'=f'*g+f*g' ... | |
| trigonometry | 9/2/2009 |
| Q: using the definitions of sine and cosine, prove that sin^2t + cos^2t = 1 A: One of the quickest way to prove it is by taking a right triangle with hypotenuse equals 1 . See ... | |
| Calculus 1 question | 9/1/2009 |
| Q: I'm having trouble evaluating the difference quotient for the given function and simply that answer, ... A: f(x)=x³ , Let's differentiate : f'(x) at x=a . Lim [ f(a+h)-(f(a) ] / h = h->0 Lim [ (a+h)³-a³ ] ... | |
| Calculus | 8/30/2009 |
| Q: Concider the Function f(x,y) = 1 + xy+x^2y^2 (a)Find the gradient vector of f(x, y) at the point ... A: B) The scalar product between the Gradient & the directional vector is zero , means that the ... | |
| MVCalculus | 8/18/2009 |
| Q: The temperature of a star decays from the centre towards the surface as T(x,y,z)= ... A: Since T(x,y,z) is a 3D function , the derivative will be not only with respect to the variable but ... | |
| Integration | 8/17/2009 |
| Q: The curve with equation y=(e^-x)(sinx) has one stationary point for which 0<=x<=pi. I) Find the ... A: Our curve is : y=[e^(-x)][sin(x)]. Let's derive using the rule : (fg)'=f'g+fg' : ... | |
| Calculus | 8/17/2009 |
| Q: The deflection H of a metal structure can be calculated using the formula H=(Sqrt(I*p^4*D^2*L^(3/2) ... A: H can be written more clearly as : H = [1/√(20g)] * √I * P² * D * L^(¾) . Now : We ... | |
| Complex numbers | 8/16/2009 |
| Q: The complex number z is given by z=(4-3i)/(1-2i). Find the two square roots of complex number 5-12i, ... A: Ok, First of all, I had a slight mistake in the last row : 2nd solution : ... | |
| Complex numbers | 8/16/2009 |
| Q: The complex number z is given by z=(4-3i)/(1-2i). Find the two square roots of complex number 5-12i, ... A: √(5-12i) will give 2 solutions. ("Dividing the unit circle into 2 pieces"). Lets 1st write the ... | |
| Integration the volume | 8/15/2009 |
| Q: The diagram shows the curve y=(e^-.5x) (1+2x)^.5 and its maximum point M. The shaded region between ... A: Let's 1st calculate ∫xe^(-x)dx : Let's denote u=x & v'=e^(-x). Therefore : ∫uv' = ... | |
| Integration the volume | 8/15/2009 |
| Q: The diagram shows the curve y=(e^-.5x) (1+2x)^.5 and its maximum point M. The shaded region between ... A: Our curve is f(x)=√(1+2x)*e^(-½x). Let's find point of intersect with x-axis : ... | |
| Complex numbers | 8/14/2009 |
| Q: The variable complex number z is given by z=2cos a+i(1-2sin a),where a takes all values in the ... A: z+2-i=2cos(a)+i[1-2sin(a)]+2-i=2cos(a)+i-2isin(a)+2-i=2[cos(a)+1-isin(a)]. 1/(z+2-i) = ½ * ... | |
| Quadratic | 8/14/2009 |
| Q: Solve the equation, e^x + e^2x = e^3x. Thanks A: e^x+e^2x=e^3x . Let's denote t=e^x , we get : t+t²=t³ . Since e^x can never be zero, we can devide ... | |
| Integration | 8/13/2009 |
| Q: the constant a is such that integration of (xe^.5x) with limits a to 0 equal to 6.Show that a ... A: The integration of exponential functions : 1. Since (e^x)'=e^x , we conclude that ∫e^x dx = ... | |
| Calculus- Minimum problem | 8/9/2009 |
| Q: I'm having a tough time with this question and would appreciate your advice. A new cottage is built ... A: 1st of all I attached a drawing to illustrate the problem . Lets denote z as the distance of ... | |
| differentiation | 8/7/2009 |
| Q: Find the answer using composite rule first? f(x)=In(1-e^-x) (i.e. 1 - e to the power of -x) (x>0) ... A: f(x)=Ln[1-e^(-x)] v=-x & u=1-e^(v) . Thus : 1. v'=-1 2. u'=-e^(v)*v'=e^(-x) Therefore : f=Ln(u) ... | |
| calculus with applications | 8/5/2009 |
| Q: findthe open intervals where the function f(x)=-3x^3+18x^2+167x-7 is concaved upwards and downwards. ... A: Infliction points is when the the derivative of f(x) say f'(x) is at extremum. The same as when ... | |
| Calculus Question | 8/4/2009 |
| Q: Water is being collected from a block of ice with a square base. The water is produced because the ... A: 1st of all , let's translate the given facts into mathematical data : If x is the edge of the square ... | |
| critical numbers help | 8/3/2009 |
| Q: I am having difficulty with the following problem. Any assistance will be greatly appreciated. ... A: To know if it's a min or max , we derive g(t) twice : g''(t)= { √(5-t)-[t/√(5-t)] } '= ... | |
| Re: Calculs | 7/30/2009 |
| Q: Find the volume of the solid obtained by rotating the region bounded by the curves ... A: π π 2π∫sinx dx + π∫sin²x dx = 0 0 ... | |
| Minimum Dimension Problem | 7/29/2009 |
| Q: A silo is to hold 10,000 cubic feet of grain. The silo will be cylindrical in shape and have a flat ... A: The silo shape is cylindrical . That means : 1. The surface area is S=2πrh+πr² ("1st term ... | |
| Re: Calculs | 7/28/2009 |
| Q: Find the volume of the solid obtained by rotating the region bounded by the curves ... A: In this section we have the formula of the volume is : π ∫π[Ro²-Ri²] dx . Where Ro ... | |
| Calculs | 7/28/2009 |
| Q: please help me out with the question below thanks. find the area of the region bounded by the ... A: Let's substitute y=0 into the hyperbola equation, this will give us the point of intersect of the ... | |
| Re: Calculs question | 7/28/2009 |
| Q: my name is attir i have one question that is attached as a image file please solve this thnks. A: π/4 ∫ Cos[x] dx Is the area under the graph that is bounded by the 4 set of points : ... | |
| Intro | 7/27/2009 |
| Q: Please I really need help with this: Differentiation: 1/3x^6(x^2-3) 5/square root 4+x 1/2square ... A: If you mean f(x)=1/[3x^6*(x²-3)] then f'(x)=1/{ [3x^6*(x²-3)]² } * {3x^6*(x²-3)}' =1/{ ... | |
| Integration | 7/26/2009 |
| Q: the constant a is such that integration of (xe^.5x) with limits a to 0 equal to 6.Show that a ... A: Ok, let's elaborate : 1st : --- ∫αe^(βx) dx = (α/β)e^(βx) . It's a ... | |
| Trigonometry, double angle | 7/26/2009 |
| Q: I know part i) but for part ii) I dont know how to find a. i) express 5sinx+ 12cosx in the form ... A: I'll answer for you both parts : I) 5sinx+ 12cosx = Rsin(x+Ø). We need to find R & Ø . We know that ... | |
| arctan x/1+x^2 again | 7/25/2009 |
| Q: I sort of understand the last suggestion.After arcsin^2 x-(integral of)1/1+x^2*arctan x, we can say ... A: Yes, if U=1+x² then du/dx=2x . But in our case du/dx=1/1+x² therefore u=Arctan[x]. Ok Dave, let's ... | |
| integration | 7/25/2009 |
| Q: I need to differentiate the following 8(5+x)/16-x2. I have used the chain rule for the denominator ... A: Well, using integration by parts will give us the same result. You started correctly : let's denote ... | |
| integration | 7/25/2009 |
| Q: I need to differentiate the following 8(5+x)/16-x2. I have used the chain rule for the denominator ... A: 1st of all lets note that (Arctan[x])'=1/(1+x²). So, we have an expression from the form of ... | |
| Calculus - ODE's | 7/23/2009 |
| Q: A spherical ball of wax melts away such that its volume decreases at a rate proportional to its ... A: V(t)=(4/3)πr³(t) & S(t)=4πr²(t). Where S is the surface area. We know that ... | |
| differentiation | 7/20/2009 |
| Q: I need to differentiate the following 8(5+x)/16-x2. I have used the chain rule for the denominator ... A: The rule for fractional derivative is : [f/g]'=[f'g-g'f]/g^2 . In our case : [ 8(5+x)/(16-x^2) ]' = ... | |
| Limit Proof | 7/20/2009 |
| Q: I am working on my summer assignment for AP Calc BC, and I am stuck on how to prove this. It is ... A: Let's prove it by the definition of limit . Reminder : Lim f(x) = 0 , means : x->c for every ... | |
| Tangents to parametrized curves | 7/17/2009 |
| Q: I'm having some trouble for this question, can you explain why I was wrong? Q: Find an equation for ... A: y=SQRT[4-x^2]=[4-x^2]^(1/2) y'=(1/2)*(-2x)[4-x^2]^(-1/2)=(-x)[4-x^2]^(-1/2) ... | |
| Tangents to parametrized curves | 7/16/2009 |
| Q: I'm having some trouble for this question, can you explain why I was wrong? Q: Find an equation for ... A: The tangent line at point (x,y)=(#2,#2) can never intersect with the axis in pint x=2 or y=2. ... | |
| Integral | 7/15/2009 |
| Q: What is the integral of log 10x? A: Log10(x)=Ln(x)/Ln(10) Integral of {Log10(x)} = Integral of {Ln(x)/Ln(10)} = [1/Ln(10)]*Integral of ... | |
| Differentiation | 7/10/2009 |
| Q: An underground storage tank is being filled with liquid as shown in the diagram.Initially the tank ... A: Ok , let's review our given facts : 1. At any given time t , the tank has an amount of liquid v(t). ... | |
| Integration | 7/10/2009 |
| Q: the constant a is such that integration of (xe^.5x) with limits a to 0 equal to 6.Show that a ... A: The integral of xe^(x/2) is 2(x-2)e^(x/2). This can be easily shown via "Integration By Parts" ... | |
| Find Equation of the Tangent Line | 7/1/2009 |
| Q: Find an equation of the tangent line to the graph of the function at the given point. f(x)= ... A: Ok, 1st of all the equation of the line will be : y=ax+b. Where a is the slope & b is the intersect ... | |
| Calculs | 6/26/2009 |
| Q: Alon, I have the equation for the instantaneous voltage during the charge of a capacitor, viz ... A: The calculus term in this section is due to the nature of the process of charging & discharging of ... | |
| curve sketching | 6/25/2009 |
| Q: I need help with this problem. Given the following function, state the domain, all asymptotes, ... A: h(x)=(4-x^2)/(x^2+1) 1)Domain : All x ("because x^2+1 is always positive") 2)Intercepts with ... | |
| Equation of Tangent Line | 6/18/2009 |
| Q: Question given: The curve y=lnx^3 has one tangent line that passes through the point (0,1). Find the ... A: Ok Julia, first I made assumption that: The Tangent Line touch the curve at point A which has an ... | |
| Equation of Tangent Line | 6/17/2009 |
| Q: Question given: The curve y=lnx^3 has one tangent line that passes through the point (0,1). Find the ... A: The 1st step you did was right, the 2nd not . The point (0,1) is not a point on the curve !!! its an ... | |
| Help me with the extreme values of the function | 6/17/2009 |
| Q: z = x2 – y + 4ln(3-x) + ln(y+2) This was problem for the exam.. and I didn't know how to solve it. ... A: z=x²–y+4ln(3-x)+ln(y+2) 1st we need to find the partial derivatives : ∂z/∂x = ... | |
| Assymptotes | 6/9/2009 |
| Q: How would I find the horizontal assymptotes algebraically for the function y=x/sqrt(x^2-4). I know ... A: y=x/sqrt(x^2-4) The vertical assymptotes are : x=2 & x=-2 . They are calculated by asking when y ... | |
| minima problem | 6/8/2009 |
| Q: sir, how can i find minima of z=f(x,y). that for what values of x and y, z will b minimum. A: 1st you need to calculate these forms : 1. ∂z/∂x 2. ∂z/∂y 3. ... | |
| Limits | 6/8/2009 |
| Q: I need to find the limit as x-->+INF for the function f(x)=(sqrt(x^2+x)-x). I having trouble with ... A: We will use the trick : √a-√b=(a-b)/(√a+√b) . This will gives us : ... | |
| Calculus | 6/8/2009 |
| Q: I need this question answered VERY soon, thank you! Generate the Maclaurin Series for f(x)=cos3x. ... A: Maclaurin Series for f(x) is defined as : f(x) ~ f(0) + f'(0)x + ½f''(0)x² + (1/6)f'''(0)x³ +...+ ... | |
| Derivative | 6/7/2009 |
| Q: I have to find, from first principles, the derivative of f(x)=sqrt(x+1). I don't know how to do ... A: Let's find the derivative by definaition : Lim [f(x+h)-f(x)]/h = f'(x) h->0 Now, our function ... | |
| Optimization | 6/6/2009 |
| Q: The hypotenuse of a right-angled triangle has the length 10 cm. Find the maximum perimeter. I'm ... A: Perimeter of right-angled triangle is P=a+b+c where c=√(a²+b²). So we know that ... | |
| limits | 6/4/2009 |
| Q: so I have a few questions about these problems. I'm not sure how to do them with x's in various ... A: lim (1+(11/x))^(x/6) = ? x->INF We know that : Lim [1+(1/x)]^x = e x->INF & we also know ... | |
| word problems. | 6/4/2009 |
| Q: 1. At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ... A: 1. I assume you took z=√(x²+y²) . Thus, dz 2x (dx/dt) + 2y (dy/dt) -- = ... | |
| equation to a tangent line | 5/31/2009 |
| Q: On the graph (x^2-5x+4)/(x^3-2x^2-8x) what is the equation for the tangent line at the point (-1,2)? ... A: The derivative is correct . & the slope is -0.92 . The equation of the tangent line is not correct!! ... | |
| graph | 5/31/2009 |
| Q: My name is Kira Yuta I am in grade eleven in USA I am studying for my final exam and I came a upon ... A: Ok Kira , let's start with section 1 : We need to write an equation for the parabola . Let's review ... | |
| Integral of absolute value function | 5/31/2009 |
| Q: I need some help with this problem: Evaluate the integral of the absolute value of (2x-3) from x=8 ... A: The function f(x)=|2x-3| can be defined also as : f(x)=-2x+3 when x<3/2 & 2x-3 when x>3/2. Thus our ... | |
| Derivatives | 5/29/2009 |
| Q: (1). how do I find dy/dx of this function: y= x^(log(6)(x)) It is log base 6 of x. I'm not sure ... A: I know why it didn't work, & I apologize. The solution is not exact. Here is the right solution, for ... | |
| Derivattion | 5/29/2009 |
| Q: I am trying to derivate an ecuation but with not much success. Could you give me a hand? This is ... A: f(x)= (1+x²)√(x-1) / (2x+1)(3x²+2x-1)^⅓ f'(x)= { 2x√(x-1)+(1+x²)/[2√(x-1)] ... | |
| Derivatives | 5/28/2009 |
| Q: (1). how do I find dy/dx of this function: y= x^(log(6)(x)) It is log base 6 of x. I'm not sure ... A: (1) y= x^(log(6)(x)) We know that Logx{Base 6}=Lnx/Ln6. Thus, we get : y=x^(Lnx/Ln6) Let's perform ... | |
| derivatives of log func. | 5/28/2009 |
| Q: How do I do these as well??? For both i need to find dy/dx. We were only taught 1 example in class ... A: y = Ln[ (3x-11) / x*(x^2+1)^(1/5) ] y = Ln[3x-11] - Lnx + (1/5)Ln[x^2+1] y'/y = 3/(3x-11) - (1/x) + ... | |
| finding the slope. | 5/26/2009 |
| Q: my question is about this problem Find the slope of the tangent line to the ellipse ... A: Slope of a curve f(x,y)=0 is defined as y'(x,y). To find y' we perform implicit derivative on the ... | |
| Question | 5/25/2009 |
| Q: This problem also I really need help on: Let f(x)=x^4-4x^3-8x^2+5 a) On what interval(s) is f ... A: f(x)=x^4-4x^3-8x^2+5 f'(x)=4x^3-12x^2-16x To find local max/min we solve f'(x)=0 : 4x^3-12x^2-16x=0 ... | |
| test help | 5/25/2009 |
| Q: So i took a test and I have the opportunity of earning credit back if I redo it.. and I need help ... A: The derivative of t/2 is 1/2 ! If s(t)=(e^(-3t))(cos(t/2)) then ... | |
| please HELP! | 5/25/2009 |
| Q: I just want to know where I went wrong with answers. Some of the questions include: 1b) 5/x^2 - ... A: Section 3 is 100% correct ! you shoud review your math teacher. In Section 1 I didn't understand ... | |
| differentiation | 5/24/2009 |
| Q: I am trying to find dy/dx of this equation: x= y ln xy Could you please give me a hand and tell me ... A: x=yLn(xy) or x=yLnx+yLny . Let's derive the equation with respect to x : That means d/dx x = 1 & ... | |
| Calculus (basic trig integrals) | 5/23/2009 |
| Q: WHY is integral of sin equal to -cos? AREA under Sin curve from 0 to Pi is POSITIVE, but values of ... A: 1st of all d/dx sin[x] = Cos[x] & not -Cos[x] !! Lets prove the derivative by definition : Lim ... | |
| Calculus Problem | 5/22/2009 |
| Q: Wondering if you can help me with this one. Part (a) asks by completing the square (and then doing ... A: ½ ∫dx/(x²-x+1) = ? 0 We know that (x²-x+1) = ¼[ (2x-1)²/3 + 1], which also means : (x²-x+1) = ... | |
| l'hospital's rule | 5/22/2009 |
| Q: my question is: how do I find the limit of this using hospital's rule? I tried doing it by finding ... A: L'hospital's rule is applied whenever we have the form : Lim [f(x)/g(x)] = 0/0 x->a Now let's ... | |
| solve the proof | 5/20/2009 |
| Q: cos3x = 4cos^3x-3cosx A: The basic rules we will use in this proof will be : 1. sin2x=2sinxcosx 2. sin²x+cos²x=1 -> ... | |
| trig. funtion proof. | 5/20/2009 |
| Q: prove the trig. function: tanx + sinx / 2tanx = cos^2(x/2) A: We know that cos(½α)=√½[1+cosα]. Thus cos²(½α)=½[1+cosα] . ... | |
| derivative and concave q's | 5/19/2009 |
| Q: For this problem, f(x)= 6x^2 ----------- x^2+16 The two q's below are the two ... A: f(x)=6x²/(x²+16) . f'(x)=12x/(x²+16) - 70x³/((x²+16)² Let's find extremum points : we solve f'(x)=0 ... | |
| derivatives with concave q's | 5/19/2009 |
| Q: For this problem: f(x)=e^(-3.5x^2) When I found the derivative I got: (e^(-3.5x^2))(-7x) I don't ... A: your derivative is right : f(x)=e^(-3.5x²) f'(x)=-7xe^(-3.5x²) ... | |
| derivatives with concave q's | 5/19/2009 |
| Q: So for this problem: 6 f(x)= ------------ ((x^2)-16) I got a critical # of ... A: f(x)=6/(x²-16). Let's calculate f'(x) & f''(x) : f'(x)=-12x/(x²-16)² & f''(x)=48x/(x²-16)³ - ... | |
| Integration ( general question ) | 5/18/2009 |
| Q: I like Math and am trying to learn integration beyond the English A levels. However, I get so ... A: Yes the integration territory is very large one & requires lots of techniques. It begins by getting ... | |
| Integrals | 5/17/2009 |
| Q: Compute each integral: 1) ∫b=4 a=1 √(1+√(x))dx and 2) ... A: 1. ∫√[1+√x] dx In this section we will use the substitute method : We set ... | |
| related rates | 5/16/2009 |
| Q: An airplane flying horizontally at an altitude of 3 miles and at a speed of 480mi/hr passes directly ... A: Your direction is correct but need to be careful : According to Pythagoras x=√[a(t)²+b(t)²]. ... | |
| higher derivatives in relation to words. | 5/15/2009 |
| Q: Consider these statements written in ordinary language: A The speed of the car is proportional to ... A: A -> s'=ks Explanation : If s(t) is the position then the velocity is the derivative. B -> s''>0 ... | |
| Please help me out with this quetion | 5/14/2009 |
| Q: integrate this; 1. cos inverse (3x)dx 2.dx/(4-9x^2)^2 3.x^2 dx/(x^2-3x+2) A: 1. ∫Arcos[3x] dx In this section we will use integration by parts : ∫dvu=vu-∫vdu ... | |
| problem understanding the meaning of it all....!!! plz help.. | 5/13/2009 |
| Q: I'm a physics student from india. I know basic calculus. No problems with that. I can differentiate, ... A: I apologize for my late reply , had a rough 2 days of work , the company is having a tied schedule ... | |
| Extreme Value Problem- sine function | 5/13/2009 |
| Q: please can you help me with the following example: Find the extreme values of the function y= ... A: Let's derive the function : y=[sin(x)]^x Lny=Ln {[sin(x)]^x} Lny=xsinx d/dx { Lny } = d/dx {xsinx} ... | |
| Calculus | 5/13/2009 |
| Q: I need help please, becuause this is my second time posting it and i hope you can solve this, thanks ... A: LEt's chick continuousity: Lim f = Lim f = Limf x->a+ x->a- x->a Lim E(r) when ... | |
| WORD PROBLEMS WITH DERIVITIVES! | 5/12/2009 |
| Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the ... A: Area of the window A :2xr+πr² perimeter of the window M ... | |
| deriv world problems. | 5/12/2009 |
| Q: A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it ... A: Suppose that x is the length of the field & y is the width . Therefore, the amount of fence will be ... | |
| calculus question | 5/12/2009 |
| Q: Suppose the height of the tide is given by the equation h(t) = 4 sin {2Pi(t+8)/P} T is measured in ... A: In order to find out minimum & maximum we derive h(t) & solve the equation h'(t)=0. Therefore, ... | |
| optimization | 5/11/2009 |
| Q: a manufacturer wants to create closed rectangular box with a square base. it costs $2 per square ... A: If we consider x as the dimensions of the base & y as the height, then the surface area of the box ... | |
| Math | 5/11/2009 |
| Q: Please help me answer this question, Carolyn drops a sandbag from the top of a tall building h feet ... A: The Sand Bag : vo=0 v=gt x=½gt² ----------- The Ball : u=uo-gt x=uot-½gt² ------------- 1. The ... | |
| Trapezoidal Rule | 5/10/2009 |
| Q: evaluate the integral e^x^2 with lower limit 1 and upper limit 2 using trapezoidal rule A: Trapezoidal Rule : b ∫f(x)dx ~ Δx[½f(xo)+f(x1)+f(x2)+...½f(xn)], where : a ... | |
| precalc | 5/8/2009 |
| Q: okay i found that I am stuck on thes questions I solved the answer to some but have no idea if they ... A: d/dx 1+cos²(½x)=-cos(½x)sin(½x) d/dx 1+½cos²x=-cosxsinx d/dx 1+½cos2x=-cos2xsin2x d/dx ... | |
| calc | 5/7/2009 |
| Q: I have a question about this problem: x^(5/11)(x-5)^2 the question is: find all the critical ... A: In this section we will follow the rule : [f(x)g(x)]'=f'(x)g(x)+f(x)g'(x). Therefore : d/dx ... | |
| calc w/ trig | 5/6/2009 |
| Q: find and classify stationary values on the curve y=sinx/2-sinx 0<or=x<or=pi A: The stationary points,are the ppints of x where dy/dx=0. If y=sin(½x)-sinx then dy/dx=½cos½x-cosx . ... | |
| integrals | 5/6/2009 |
| Q: find the integral of ln(x^2+1) using integration by parts. Can you please explain how this can be ... A: Integration by parts rule : ∫u'(x)V(x)dx=u(x)v(x)-∫u(x)v'(x)dx. In our case u'(x)=1 & ... | |
| integrals | 5/4/2009 |
| Q: just a bit stuck on these (a) Integrate 1/(x(lnx)^3) with repsect to x, using the substitution ... A: The trick is this : 3/[(x+5)(x-2)] = a/(x+5) + b/(x-2). Now we have to find a & b : a/(x+5) + ... | |
| integrals | 5/4/2009 |
| Q: just a bit stuck on these (a) Integrate 1/(x(lnx)^3) with repsect to x, using the substitution ... A: (a)∫dx/(xLn³x) = ? If u=Lnx then du=dx/x , thus dx=xdu=e^u du. Hence, ∫dx/(xLn³x) = ... | |
| calc | 5/4/2009 |
| Q: how do I graph these?? I got most of this right but I need to graph this as ONE function. 1. lim ... A: Lim f(x) = -2 x->∞ f(x)=(1/x) - 2 or f(x)=e^(1/x) - 2 or f(x)=-2x/(x+1) . ... | |
| calc | 5/4/2009 |
| Q: how do I graph these?? I got most of this right but I need to graph this as ONE function. 1. lim ... A: 1. Lim f(x)=-2 x->∞ ANS : f(x)=2+(1/x) 2. Lim f(x)=2 x->-1 ANS : f(x)=(1-x²)/(x+1) ... | |
| derivatives | 5/2/2009 |
| Q: (a) Find the derivative of x^(x^2) (x to the power of x to the power of 2) (b) find the ... A: [x^(x^2)]'=? The method here is to perform Ln for both sides & then take derivative with respect to ... | |
| getting ready for next ch. | 4/30/2009 |
| Q: anything you can answer REALLY DOES HELP! So first part is: 1. to this trig identity, ... A: 1. Lim [Sin(x+h)-Sin(x)]/h = h->0 Lim [sin(x)cos(h)+cos(x)sin(h)-sin(x)]/h = h->0 Lim { ... | |
| Calculus | 4/29/2009 |
| Q: By cutting away identical squares from each corner of a rectangular piece of cardboard and folding ... A: If the corners were cut x inches deep, then the volume of the box will be : V=6x(16-2x). To max we ... | |
| pre calc | 4/29/2009 |
| Q: I need help understanding the answers 1. Which of the following is true about the graph of ... A: 1. f(x)=(x-2)/(x^2-2x) This function can be written also as : f(x)=(x-2)/x(x-2)=1/x. The function ... | |
| Calculus Problems | 4/28/2009 |
| Q: 1. A large bin for holding heavy material must be in the shape of a box with an open top and a ... A: I'll solve the 1st problem & I will leave the other 2 , for you as an exercise : The Area of the ... | |
| Calculus limit... anf continiuty | 4/28/2009 |
| Q: .. can you help me from this problem... i cant solve this during my exam on calculus yesterday.... i ... A: Continuousity means : Lim f(x) = Lim f(x) = Lim f(x) x->α+ x=α- ... | |
| need a help with my home work | 4/27/2009 |
| Q: A polluted river with a nutrient concentration of 100 g/m^3 is flowing at a rate of 100m^3/day into ... A: Let's 1st of all build the diffEqua of the Amount of nutrient is the estuary N(t) : To do so, we ... | |
| Integration problem | 4/26/2009 |
| Q: How do you find the integral of [sin^2(3x)]*[cos^2(3x)]? (integral sin squared of 3x times cos ... A: Let's review some of the facts regarding sin & cos : 1. Cos(2Ø)=2Cos²(Ø)-1 --> Cos²(Ø)=[1+Cos(2Ø)]½ ... | |
| averages problem | 4/24/2009 |
| Q: I have a problem with a maths homework question. If you know the average duration (in days) a large ... A: Sorry it took me little bit long to reply, I just had some extra work to do in my company, & for ... | |
| improper multiple integral | 4/22/2009 |
| Q: I have a question about a problem that's in the multiple integrals in polar coordinates, but doesn't ... A: ∫∫ e^-(x²+y²) dxdy Can also be written as : ∫∫ e^(-x²)*e^(-y²) dxdy . This ... | |
| CALC | 4/21/2009 |
| Q: If an arrow is shot straight upward on the moon with a velocity of 58 m/s, its height (in meters) ... A: First of all , let's review some facts : 1. The velocity of the arrow as function of time is : ... | |
| Max/Min and implicit differentiation | 4/20/2009 |
| Q: I am stuck on two problems and I was wondering if you could help me. I am recently getting back into ... A: (1) Find Max/Min on the function f(x)=sin^2x + cosx : f'(x)=2sinxcosx-sinx. Extremum points ... | |
| Calculus,tangent line | 4/19/2009 |
| Q: Find an equation of the parabola y=ax^2+bx+c that passes through (0,1) and is tangent to the line ... A: Let's run through the given fact & calculate a,b & c : (1)The parabola passes through the point ... | |
| Calculus | 4/18/2009 |
| Q: A wire of length 12in can be bent into a circle, bent into a square, or cut into two pieces to make ... A: Suppose that x is the amount of wire to creat a circle, then y is the amount of wire to create a ... | |
| Several questions I am having difficulty with? | 4/18/2009 |
| Q: I nbeed to know not only the answer to the following questions bu t how to work them. What is the ... A: (1) f(x)=x³+5x²+3x+4. To find extremum we derive & solve the equation f'(x)=0 : ... | |
| Calculus | 4/17/2009 |
| Q: A spherical tank contains 81.637 gallons of water at time t = 0 minutes. For the next 6 minutes, ... A: The equation will be : 6 V(t)=81.637-∫ v'(t)dt 0 6 ... | |
| math modeling and integration | 4/16/2009 |
| Q: I have a relative growth function 1/P∙dP/dt= b + aP where a = -.00009175 and b = .02866 and P ... A: (1/P)∙[dP/dt]=b+aP dP/dt=bP+bP² dP dt ------- = ---- bP+bP² 1 ... | |
| Calculus | 4/16/2009 |
| Q: for f(x) =e^-x sinx find all intervals of increasing and decresing, all relative extrema, intervals ... A: f(x)=e^(-x)*sinx f'(x)=-e^(-x)*sinx + e^(-x)*cosx f'(x)=e^(-x)[cox-sinx] f'(x)=0 -> cox=sinx -> ... | |
| Calculus | 4/16/2009 |
| Q: Optimization: Suppose that the sum of the surface areas of a sphere and a cube is constant. Show ... A: S1 : SurAr(cube)=6x² S2 : SurAr(sphere)=4πr² S1+S2=Const=C Now let's find a relation between x ... | |
| Calculus | 4/15/2009 |
| Q: i am in a calculus class and i need help in a homework question please. Thanks.L'Hospitals rule: ... A: Lim x[k^(1/x)-1] = x->∞ Lim (1/t)*(k^t)-1 = t->0 Lim [ (k^t)-1 ] / t = t->0 Lim ... | |
| problems to solve step by step | 4/15/2009 |
| Q: 1. 2 ln x =1 2. ln(5-2x)=3 3. ln x +ln(x-1)=1 4. ln(ln x)=1 A: Ok, let's review some of the facts concering Ln function : 1. Ln(e)=1 2. Ln(ab)=Ln(a)+Ln(b) 3. ... | |
| calculus | 4/13/2009 |
| Q: 1) Suppose that a square sheet of aluminum is placed in the hot sun. It begins to expand very slowly ... A: 1) The relation between the diagonal d & the length x is d=x√2. Thus, x=d²/4. The area S=x² & ... | |
| Minimum Optimization | 4/13/2009 |
| Q: A square bottomed box with no top has a volume of 500 cubic feet. What dimensions minimize the ... A: Surface Area S=x²+4xy , where x is the length of the base , & y is the hieght of the sides. We also ... | |
| Stokes' Theorem | 4/11/2009 |
| Q: Applying Stokes' Theorem, evaluate the integral ∫((y^2-z^2 )dx+(z^2-x^2 )dy+(x^2-y^2)dz) ... A: ok, 1st of all , lets write the technique to Stokes' Theorem : ∫∫ROt(F)ds = ∫Fdr s ... | |
| Trigonometric Differenciation | 4/9/2009 |
| Q: I was just wondering if you could help me answer these differentiation problems. I tried to ... A: 1. y=4[sin³(x²)] -> y'=4[sin³(x²)]'= 4*3[sin²(x²)]*cos(x²)*2x = 24x[cos(x²)]sin²(x²)]. I ... | |
| Computing Wind Speed | 4/7/2009 |
| Q: Tail wind, a small piper craft can fly 600 miles in 3 hours. Against same wind, it can fly same ... A: Let's set u=Velocity of the craft & v=Velocity of the wind. When the craft is flying constant in the ... | |
| Integrate | 4/5/2009 |
| Q: .. x + 2x^3/(x^4 + X^2) dx sin^2 x cosx dx sin /1 - sin^2 t dt A: ∫sint/(1-sin²t) dt = ∫sint/(cos²t) dt . We know that ... | |
| Integrate | 4/5/2009 |
| Q: can u please show da steps on how to integrate a few questions... x^5 - 2x^3 + 5/x^2 dx 1/sqrtx(1 + ... A: (1) ∫ {x^5 - 2x^3 + 5/x^2} dx = ? In this integral I will use 2 basic rules : a. ∫ax^n ... | |
| Implicit differentiation and linearization | 4/4/2009 |
| Q: The function f(x)changes values when x changes from a to a +dx. What is the approximation error of ... A: I'll start with implicit derivatives & implicit function. To derive a function which is given in an ... | |
| related rates | 4/3/2009 |
| Q: a potter places a cylindrical lump of clay on her wheel. before she begins to shape it the ... A: During the shaping process , the surface area (the amount of lump) doesn't change. That means, at ... | |
| Derivative at a Point | 4/2/2009 |
| Q: The function f(x) = tan(3^x) has one zero in the interval [0,1.4]. The derivative at this point is ... A: f(x) = tan(3^x) f(x)=0 -> tan(3^x)=0 -> 3^x=π -> x=Ln(π)/Ln(3)=1.04 this is the zero ... | |
| Equation of Normal Line To Curve | 4/2/2009 |
| Q: The equation of the normal line to the curve y = (x^2 - 1)^(1/3) at the point where x = 3 is a. y ... A: Our curve is y = (x^2 - 1)^(1/3) . Therefore , y'=(1/3)(x^2-1)^(-2/3)*(2x)=(2x/3)/(x^2-1)^(2/3). ... | |
| calculus | 3/31/2009 |
| Q: determine the volume of the solid of revolution obtained when the curve: f(x)=x^2+2 is rotated one ... A: Volume of revolution is : V=π∫f²(x)dx. In our case : 2 V=π∫(x²+2)²dx = ... | |
| Calculus III - intersection of a plane and a sphere | 3/29/2009 |
| Q: The intersection of a plane and a sphere is a circle. So how do you obtain the equation of the ... A: I have to disagree with you. The intersection of any intersecting plane and a sphere is an ellipse. ... | |
| Min/Max problems | 3/22/2009 |
| Q: A farmer wishes to fence off three identical adjoining rectangular pens, each with 300 square feet ... A: Let x be the length of each rectangular & y the width. From the drawing attached we conclude that ... | |
| Implicit Differentiation Help! | 3/21/2009 |
| Q: 1. Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at ... A: I will solve (2) & (5) , the others I will leave it for you as an exercise : -3x^2-4xy-2y^3=-12 ... | |
| calculus | 3/18/2009 |
| Q: I am Ssa. For a function f(x,y) to be differentiable, its partial derivatives have to be defined ... A: The function x^2 is always continuous for all x , the same as for the function y^2 for all y. Thus, ... | |
| Minimizing Cost | 3/18/2009 |
| Q: I am having a time with this question, please help. A design for a bus stop shelter has 2 square ... A: The total material required is : A=2(Side)+1(Top)+1(Base). If we set x as the length of each side, & ... | |
| Mathematics for Pharmacy (PHMA 101) | 3/16/2009 |
| Q: HOW DO WE INTERGRATE BY SUBSTITUTION? CAN I PLEASE HAVE A FEW EXAMPLES EXPLAINING HOW WE DO THAT A: This method is very useful specially when the integrand contains powers. For example : 1 ... | |
| Prolem | 3/15/2009 |
| Q: I have a problem that says : express sin11pi/12+sin5pi/12 as a product and find the exact value of ... A: Let's use the Trigonometric Identity : ... | |
| limits | 3/9/2009 |
| Q: lim x-> 4 sqrtx- 2/x-4 lim x-> 2 1/x-1/2/x-2 lim x-> infinity x^3/ x^4 +9 lim h -> 0 (4+h)^2 -16 ... A: Lim (√x -2)/(x-4) = Lim [(√x -2)*(√x +2)]/[(x-4)*(√x +2)] = x->4 ... | |
| predicting position in a damped oscillatory system | 3/7/2009 |
| Q: I hardly know any calculus or differential equations so I'll need a complete answer. I've tried ... A: Yes, there is no calculus involved in your problem, it's much more Differential Equations combined ... | |
| Surface area | 3/7/2009 |
| Q: I have tried both these problems several different ways and have yet to come up with a correct ... A: # A spherical balloon is being inflated uniformly. ------------------------------------------------- ... | |
| Derivatives | 3/4/2009 |
| Q: What is the derivative of Y= secx/x and the derivative of y=cosx/1+sinx. Thanks, A: y=(sec[x])/x To derive y , we will follow these rules : 1. Sec[x]'=Sec[x]*Tang[x] 2. ... | |
| Calc 2 evaluating improper integrals | 3/4/2009 |
| Q: evaluate the improper integrals or show that it diverges. 1. integral from 0 to 9 of ((e to the sq. ... A: Let's start with section 2: ∞ ∫ (x+1)/x dx 1 We will use the rule : If f(x)>g(x) in ... | |
| fourier transform | 3/1/2009 |
| Q: for the fourier transform attatched I need to determine expressions for the amplitude and phase of ... A: Sure, first of all let's review some of relevant facts : 1. ... | |
| fourier transform | 2/26/2009 |
| Q: for the fourier transform attatched I need to determine expressions for the amplitude and phase of ... A: G(w)=[20/√(2π)]*[1/(401-w²+2jw)] is a complex variable. To find absolute value & phase, ... | |
| a+bi | 2/25/2009 |
| Q: how do i get standard form (a+bi) from this... 2(cos(pi/4)+isin(pi/4) That is the polar form ... A: The transfer rule from polar to Cartesian is : Z=a+ib <--> Z=ρe^(iθ) Where : ... | |
| Math (related rates) | 2/25/2009 |
| Q: A rectangle is expanding so that its length is always twice its width. The perimeter of the ... A: Suppose that the dimensions of the rectangle are x(t) & y(t). We know that the perimeter M is M=x+y ... | |
| fourier series | 2/23/2009 |
| Q: need some help with the following question. Determine the fourier series of the signal f(t) = 1+t/pi ... A: In terms of fourier series, our signal f(t) will be : f(t) ~ 1 + [4/π²]cos(t) + ... | |
| Integration | 2/21/2009 |
| Q: I have been working on this integration problem, but I'm not getting anywhere. Could you show me the ... A: To solve this integral we will use 2 basic rules : 1. d/dx Ln[h(x)]=h'(x)/h(x) 2. d/dx ... | |
| fourier series | 2/19/2009 |
| Q: need some help with the following question. Determine the fourier series of the signal f(t) = 1+t/pi ... A: 1. a(n)=(1/π)∫[1+(t/π)]cos(nt)dt {t goes from -π<t<π} = ... | |
| solve equation | 2/18/2009 |
| Q: (x^2 - 5x + 5)^x^2+9x+20 = 1 A: I suppose you mean : (x²-5x+5)^(x²+9x+20)=1. In this case , we perform Ln operator to both sides : ... | |
| fourier series | 2/17/2009 |
| Q: need some help with the following question. Determine the fourier series of the signal f(t) = 1+t/pi ... A: The Fourier series for f(t) -π<t<π is ao/2 +∑a(n)cos(nt)+b(n)sin(nt) Where n goes ... | |
| Calculus World Problems | 2/14/2009 |
| Q: 1The number of bus riders from the suburbs to downtown per day is represented by 1200(1.50-x), where ... A: #2 N'(t)=30-2t. N'(t)=0 -> t=15 min. N(15)=30*15-15*15=225. #3 Coast=x*15+y*10 According to ... | |
| Calculus | 2/12/2009 |
| Q: For each of the following fuinctions from S to R (with f(x) being set to 0 whenever the definition ... A: f:S->R 1)f(x)= (x sin (1/x)) - 2x ; S=( -infinite, + infinite) f is not continous on its domain S; ... | |
| calculus | 2/10/2009 |
| Q: pi/2 sin^2x s ------------ dx 0 sqrt 1-cos^2 please evaluate this integral.wherepi/2 and 0 are ... A: I suppose the integrand is : (Sin[x])^2 / Sqrt[1-(Cos[x])^2]. It can also be written as ... | |
| calc | 2/10/2009 |
| Q: consider the curve defined by y^4=y^2-x^2 verify that dy/dx= x/y-2y63 write the equation for any ... A: Let's derive both sides with respect to x, keeping always in mind that : 1. dx/dx=1 2. dy/dx=y' ... | |
| Volume problem | 2/10/2009 |
| Q: Hey Alon, The following is a question I need help on. I would be great it if you could solve it in ... A: The volume of revolution along the x-axis for a curve y=(x) is defined to be V=π∫y²(x)dx. ... | |
| integral calculus | 2/9/2009 |
| Q: 0 sin w S ------------ -pi/2 (3+2cosw)^2 evaluate the integral where (s) is the sign of ... A: In this integral we will use the deriving rule : [1/f]'=-f'/f². In our case f=3+2cos(w). Therefore ... | |
| Particle Motion | 2/8/2009 |
| Q: A particle moves along the X-axis so that at time t its position is given by x(t)=sin(pi*t^2) for -1 ... A: a) Velocity is the derivative of the position : v(t)=x'(t)=2πt*cos(πt²) b) Acceleration ... | |
| diverging sequence | 2/7/2009 |
| Q: I'm stuck on a question about proving that a sequence does not converge to any limit. the sequence ... A: Ok, first of all we do agree that : 2^n > n . It's easy to prove. Now, the definition of a non ... | |
| Calculus-horizontal component | 2/5/2009 |
| Q: A point is moving along the curve y=6e to the power of X squared over 4 in such a way that the ... A: our curve is y=f(x). That means : dy/dt=(dy/dx)(dx/dt).We know that dx/dt=3 & dy/dx=y'(x). Thus, ... | |
| calculus | 2/3/2009 |
| Q: let f be the function given by f(x)=3x^4+x^3-21x^2: a. write the equation of the line tangent to the ... A: a) The tangent line equation is : (y-y1)/(x-x1)=f'(x1). Where x1=2 & y1=-28. In our case ... | |
| calc | 2/2/2009 |
| Q: find 1st and 2nd derivative of f(x)=ln(2x)/x^3 A: f(x)=[ln(2x)]/[x^3] To derive this function we use 2 basic rules : 1. LN[g(x)]'=g'(x)/g(x). 2. ... | |
| Follow-up on Surface of cylinder to sphere | 2/2/2009 |
| Q: but it seems, I still had problems with the notation, so I am writing this follow up in a new ... A: The solution 5.25 is gained when we set R=5. To present a numerical graph we need to insert ... | |
| max- min optimization | 2/1/2009 |
| Q: a lighthouse is 8 miles off a straight coast and a town is located 18 miles down the seacoast. ... A: Let's set y as the distance from the dock to the town. The amount of time t for the supplies will ... | |
| ? | 1/31/2009 |
| Q: in the expression y = 63t e^(-64t) the variation of y and time (t) gives a critically damped type of ... A: If y=63te^(-64t) then dy/dt=y'(t)=63e^(-64t)-(63*64)te^(-64t). y'(t)=0 -> ... | |
| Integration using substitution | 1/31/2009 |
| Q: Use the substitution u=x+2 to find [integral of (x^3)/((x+2)^2)dx]. I am unsure how to use the ... A: ∫(x^3)/[(x+2)^2] dx. Let's set u=x+2 . We may see that du=dx. Now, we will switch x by u-2 & ... | |
| Deriving 2e^x | 1/29/2009 |
| Q: I would like to know how to derive 2e^x? Thank you A: The derivative of e^x is e^x .. Let's prove that : y=e^x. Lets perform Ln for both sides , we get : ... | |
| Calculus | 1/27/2009 |
| Q: Ok this is integration by parts the Function is &=integration sign &e^2x(sin3xdx) u= sin3x dv= ... A: First let's see the answer of the book : 13/4 I=(1/2)e^2x sin3x-(3/4)e^2xcos3x+ C That means, ... | |
| Calculus | 1/23/2009 |
| Q: A model for the growth of a bacterial culture is given by N(t)= 2+sin^2t+sint for 4<t<8.5 where ... A: a) sin2t-cost < 0 --> 2sin(t)cos(t) < cos(t) --> sin(t) < 1/2 That gives us 4<t<6.8 & 7.85<t<8.5 b) ... | |
| Calculus | 1/22/2009 |
| Q: Need help finding a formula for the inverse of the function. f(x) = 4x - 1 ------ ... A: Ok Evan, the trigger for finding the inverse function, is to switch places between x & y. For ... | |
| Calculus | 1/22/2009 |
| Q: You are living in a time before Newton and Leibniz. One night as you sleep, you have a dream ... A: a) (x^2/27^2)+y^2=1 -> y^2=1-(x^2/27^2) -> y=√[1-(x/27)^2]. We know that x=27cosθ so ... | |
| 2 Questions on Limits | 1/20/2009 |
| Q: I have these 2 questions on limits. I get half way through factoring before getting stuck... 1) lim ... A: lim (1/t)[1/(t+4)-1/4]= t->0 lim (1/t)[(4-t-4)]/[4(t+4)]= t->0 lim (1/t)[-t/[4(t+4)]= t->0 lim ... | |
| Max and Min | 1/19/2009 |
| Q: Given an open-top box with a rectangular base x by y units and rectangular sides with depth z units ... A: We know that the volume V=xyz. We also know that the surface S=2xy+2xz+2yz=2xy+2z(x+y). The amount ... | |
| calculus | 1/18/2009 |
| Q: "Hi, Can you please help me with this question. K(x)=(2x^2+4x)e^-x I need the first, second ... A: K(x)=(2x^2+4x)e^(-x) 1)intercept points : K(x)=0 -> 2x^2+4x=0 -> x^2+2x=0 -> x=0 & x=-2. ... | |
| calculus | 1/15/2009 |
| Q: Water is draining at the rate of 48pi ft^3/sec from the vertex at the bottom of a conical tank whose ... A: Ok Sara, let's set R=40 & H=60. At a certain time, the surface of the water is at a certain level h ... | |
| Applied Maximum Problem Surface area of cylinder | 1/9/2009 |
| Q: I have a problem here which asks me to find the dimensions of the right-circular cylinder of ... A: I agree that r=√[R²-(h²/4)] or r=(½)√[4R²-h²]. Our target function is ... | |
| Calculus | 1/6/2009 |
| Q: a box in the shape of a rectangular prism has a square bottom and is open on the top. the material ... A: The total material of the box is compounded of : 4 sides & 2 bases. If we consider x is the length ... | |
| Calculus | 1/6/2009 |
| Q: Use the limit definition to find the area of the region bounded by the graph f(x)=x^2+2 the x axis ... A: According to the definition : 1 ∫ f(x)dx = 0 Lim h * [ Σ f(rh) ] where r goes from 0 ... | |
| related rates- Thanks for your help!! | 1/2/2009 |
| Q: Let V be the volume of a circular cylinder having a height h and a radius r, and assume h and r vary ... A: The volume of the circular cylinder v is v=Πhr². In our case, it will vary with time, meaning ... | |
| implicit 2nd differentiation using calculus | 1/2/2009 |
| Q: I am very new to calculus and i would love to get some help. I have a question that i cannot ... A: In Implicit derivative we retreat y as a function of x, & we derive y as well as we derive x. 2 ... | |
| Calculus | 1/2/2009 |
| Q: A PARTICLE MOVES on the x-axis in such a way that its position at time t is given by ... A: The particle is at rest when x'(t)=0 , & the particle is moving to the left when x'(t)<0. So 1st ... | |
| math | 1/2/2009 |
| Q: evaluate the line intergralof integration over c ((xy+x+y)dx+(xy+x-y)dy) ,when c is the circle ... A: Line Integral Li=∫M(x,y)dx+N(x,y)dy = ∫M(t)(dx/dt)+N(t)(dy/dt) dt where ... | |
| Tanagent | 12/31/2008 |
| Q: Please, 1. The tangent point between g(x)=ax^2+bx+c and f(x)=mx+n is x1 resp y1. What's the slope ... A: Lets find a relation between {x1,y1,m,n,a,b,c} : 1st of all if f(x)=mx+n is a tangent line to the ... | |
| calculus related rates | 12/31/2008 |
| Q: The volume of a cube of ice is decreasing at a constant rate of 10 cubic centimeters per minute. ... A: Let L be the length of an edge in the cube. Then the volume of the cube will be V=L^3. That means ... | |
| math | 12/31/2008 |
| Q: evaluate the line intergralof integration over c ((xy+x+y)dx+(xy+x-y)dy) ,when c is the circle ... A: According to the green's theorm : ... | |
| Related Rates | 12/31/2008 |
| Q: A canoe is being pulled toward a dock by a rope attached to its bow and passing through a docking ... A: Let's 1st remember the rules of square root deriving : 1. (√x)'=1/2√x 2. ... | |
| Related Rates | 12/30/2008 |
| Q: A canoe is being pulled toward a dock by a rope attached to its bow and passing through a docking ... A: Let x be the distance between the dock & the canoe. Let z be the length of the rope. Then, ... | |
| Related Rates | 12/30/2008 |
| Q: A girl is flying a kite at a height of 320 ft. If the wind blows the kite horizontally at a rate of ... A: The Length of the string is z=√(320^2+x^2). Where x is the horizontal distance caused by the ... | |
| Help on calculus please! ASAP | 12/18/2008 |
| Q: 1. f(x) = x^3 - 6x^2; find where is the function decreasing 2. f(3) = 2, f"(3)= 1/3, g(3) = 6, g'(3) ... A: 1. f'(x)<0 -> 2x^2-12x<0 -> x^2-6x<0 : 0<x<6 2. h'(3)=[f'(3)g(3)-f(3)g'(3)]/f(3)^2 = 2 3. ... | |
| calculus problems | 12/16/2008 |
| Q: I need to find the following indefinite integrals and am having trouble. Can you please help? I'm ... A: I'll start from the second : (x^3-6x-20)/(x+5)= x^3/(x+5)- 6x/(x+5) - 20/(x+5). 1. ... | |
| Curve in calculus | 12/14/2008 |
| Q: Given the curve x^2 - xy + y^2 = 9 a. Write a general expression for the slope of the curve b. Find ... A: The slope of the implicit curve is calculate as an implicit derivative of the implicit function x^2 ... | |
| logs | 12/12/2008 |
| Q: Can you possibly help me? I've been asked to simplify 2logx - 4log3 + 5logy Not only have I no idea ... A: Let's refresh our memory with the facts regarding Log function : 1. Log(a*b)=Log(a)+Log(b) 2. ... | |
| AP Calculus Derivative Question | 12/11/2008 |
| Q: I have these following questions I need answered. We were asked to find the derivative of: x^2 - xy ... A: First of all dy/dx is not -2x/(y-x) it's (y-2x)/(2y-x). & here's why : d/dx {x^2 - xy + y^2 = 28} = ... | |
| Differentiate each equation implicityly | 12/11/2008 |
| Q: e^2xlnsquarerootofy- ln(e^2x)Xe^lny = xy i am so confused on this problem A: When we are performing implicit derivatives , we have to keep in mind two major rules : 1. if ... | |
| Area under a curve | 12/10/2008 |
| Q: a polynomial of degree 2 with a negative leading coefficiant has two distinct roots r1 and r2. Find ... A: The general formula of a strait line is : (y-y1)/(x-x1)=m. Where m is the slope, & (x1,y1) is the ... | |
| Composite Function | 12/10/2008 |
| Q: Let K(x)be a composite function defined as K(x)=F(G(x)). Find K'(3)if X F(x) F'(x) G(x) G'(x) ... A: x F F' G G' 1 2 5 -3 5 2 3 1 ... | |
| need help on sinusoidal functions | 12/8/2008 |
| Q: Hey Sir, I have a question on which I need your help, If you could please take a look at it..i ... A: The general sinusoidal function is from the of : B+Asin(ωt). From the image I attached , you ... | |
| Volume of Rotation | 12/8/2008 |
| Q: The function f is denoted by f(x)= (ln(x))/(x^3), x >or= 1. The region enclosed by the x-axis, the ... A: No Problem Kaela, here's the method of integration : I will use the substitute method, where u=lnx. ... | |
| Double integral | 12/8/2008 |
| Q: Evaluate ∫(INT 8 to 2) ∫(INT 16x to 9) (3xy)^.5 dy dx I'm having a bit of trouble ... A: 2 9 ∫ ∫ √(3xy) dy dx = 8 16x 2 9 ∫ dx ∫ ... | |
| Volume of Rotation | 12/7/2008 |
| Q: The function f is denoted by f(x)= (ln(x))/(x^3), x >or= 1. The region enclosed by the x-axis, the ... A: The equation for volume of the solid of revolution is : V=π∫[f(x)]^2 dx. Where x goes ... | |
| Rate of Change | 12/7/2008 |
| Q: A spherical balloon is being inflated. Its radius in centimeters after t minutes is given by r(t)= 3 ... A: The form [f(x+h)- f(h)]/h is good when you are requested to calculate rate of change from x1 to x2. ... | |
| calculating maximum length of arc on projectiles | 12/5/2008 |
| Q: Am jammed with this , I have been asked to calculate the maximum length of the arc of a projectile ... A: Ok, our projectile has the form r(t)=[Voxt,Voyt-(g/2)t^2]. (" g is 9.8m/sec^2 "). Thus, ... | |
| Angular Velocity | 12/4/2008 |
| Q: A truck driver travels at 60 miles per hour. The truck tires have a diameter of 26 inches. What is ... A: Let's 1st converse units : 1 [inch] = 0.0254 [meter]. 1 [mile] = 1609.334 [meter]. 60 [mile/hour] = ... | |
| Line Integrals | 12/1/2008 |
| Q: Find the work done by the force field F in moving an object from P to Q. F(x,y)=e^-y i-xe^-y j ... A: The definition of work is ∫F(x(t),y(t)).r'(t)dt. Where r(t) is the path from point a to point ... | |
| Pre calculus help | 12/1/2008 |
| Q: My problem is to multiply (5 cis 100 degrees) (4 cis 230 degrees). I have to express the answer in ... A: This presentation of complex numbers is called polar. Let's refresh our memory regarding complex ... | |
| Min/Max problems | 12/1/2008 |
| Q: Find the point(s) on the hyperbola x²-y²=4 that is closest to the point (1,3) A: This question was sent to the question's pool. But I see that no one had solved it, so I decided to ... | |
| Min/Max problem | 11/29/2008 |
| Q: Find the maximum possible area of an isosceles triangle where the two equal sides are both 6cm long. A: Suppose that the isosceles triangle has : 2 isosceles sides : 6,6 base : 2x height : h According to ... | |
| Min/Max problem | 11/29/2008 |
| Q: A triangle is inscribed in a semi-circle of radius 10 cm so that one side is along the diameter. ... A: Since the inscribed triangle has the diameter as one side, & the parallel angle is on the perimeter ... | |
| Min/Max problem | 11/29/2008 |
| Q: Find the maximum possible area of an isosceles triangle where the two equal sides are both 6 cm ... A: Suppose that the isosceles triangle has : 2 isosceles sides : 6,6 base : 2x height : h According to ... | |
| Calculus Derivatives | 11/29/2008 |
| Q: Working some practice problems over the Thanksgiving break! Fun times eh? This one has me stumped: A ... A: Heather, the calculation you attached was perfectly kind of correct with 2 mistakes : 1st : ... | |
| Calculus Derivatives | 11/29/2008 |
| Q: Working some practice problems over the Thanksgiving break! Fun times eh? This one has me stumped: A ... A: sometimes a math break is needed during holidays.. Let's review a very helpful rule : d/dt { f(x,y) ... | |
| Calculus question | 11/29/2008 |
| Q: Given the function f(x)=e^-x^2 (a). Find the derivative of f (b). Find the critical values (c). ... A: Ok Melissa, you got the derivative right. To find critical points we must set f'(x)=0. That means ... | |
| calc | 11/26/2008 |
| Q: Your company is mass-producing a cylindrical container. The flat portion (top and bottom) costs ... A: Amount of flat portion F=2π*r^2. Amount of curved portion C=2*π*r*h. Costs of flat : ... | |
| calc. | 11/25/2008 |
| Q: 1. Let f be the function defined by f (x) = 3x5 − 5x3 + 2 . (a) On what intervals is f ... A: f(x)=3x^5−5x^3+ 2 . (a) function f is increasing in the intervals where f'(x)>0. ... | |
| last part of my homework, PLEASE HELP! | 11/24/2008 |
| Q: A particle moves in the plane along a curve C with representation. r(t)=tcos(t)i+tsin(t)j for ... A: C=|x'(t)y''(t)-x''(t)y'(t)|/[(x'(t)^2+y'(t)^2]^(3/2). In our case x(t)=tcos(t) & y(t)=tsin(t). So, ... | |
| Applied Max/Min | 11/24/2008 |
| Q: A rectangular storage container with a closed top is to have a volume of 24 meters cubed. the length ... A: To find the cost of materials for the cheapest container, we must 1st find the dimensions of such ... | |
| optimizing | 11/23/2008 |
| Q: .. Im hoping you would help with problem i tried so many times to do but im glad i did the rest of ... A: Let's review some of the facts : 1. The area of the two base is : B=2*π*r^2 2. The area of the ... | |
| calculus optimization | 11/22/2008 |
| Q: A pipeline must be laid from point a to point b. Point b is located 31 miles east and 40 miles north ... A: Ok, let's suppose that the point on the shore line is x miles north from point a. So , the coast ... | |
| calculus help again :( | 11/22/2008 |
| Q: Let: F(x,y)=(6xy²-3x²)i+(6x²y+3y²)j show that F is conservative and find a potential function of ... A: If F(x,y)=F1(x,y)[i]+F2(x,y)[j], then F is conservative , if & only if ... | |
| calculus help! | 11/22/2008 |
| Q: A particle moves in the plane along a curve C with representation. r(t)=tcos(t)i+tsin(t)j for ... A: a. Tangent Unit : T=r'(t)/|r'(t)|= d/dt{tcos(t)i+tsin(t)j}/|d/dt{tcos(t)i+tsin(t)j}|= ... | |
| sum of infinite series | 11/21/2008 |
| Q: i need to find the sum of the series (2+(-1/3)^n)/2^n from n=0 to inf. i really have no idea how to ... A: ∞ ∑ { [2+(-1/3)^2]/2^n } = n=0 ∞ ∑ { 2/2^n+(-1)^n/6^n } = n=0 ∞ ... | |
| Implicit differentiation | 11/20/2008 |
| Q: I have tried and i'm stuck, i dont know what kind of formula 2 use anymore..Cn u help me? I'm doing ... A: -2y didn't become -2y'-2y'. -2y becomes -2y'. The 2nd -2y' came from the next form. Here, I will ... | |
| Mechanical Design | 11/20/2008 |
| Q: The endpoints of a movable rod of length 3 feet have coordinates (x,0) and (0,y). The position of ... A: Ok Melinda, first of all rod means a stick, & this stick is located diagonally on the x-y axis (see ... | |
| Absolute max and min, inflection points, and determine whether or not they're in the interval | 11/20/2008 |
| Q: y= 3x^2-12x+5 A: 1st of all this quadratic equation has 1 critical point , that can be max or min depends on the 2nd ... | |
| Implicit differentiation | 11/19/2008 |
| Q: I have tried and i'm stuck, i dont know what kind of formula 2 use anymore..Cn u help me? I'm doing ... A: Ok , let's review some of the facts regarding implicit function derivatives : 1. d/dx {x} = 1 2. ... | |
| calculus | 11/19/2008 |
| Q: let f be the function given bbby f(x)= x^3-5x^2+3x+k where k is a constant 1- on what intervalls is ... A: f(x)= x^3-5x^2+3x+k 1. Let's find the derivative of f: f'(x)= 3x^2-10x+3, now we set it equal zero ... | |
| Second derivatives | 11/19/2008 |
| Q: I'd like to better understand the process of getting second derivative of rational functions such as ... A: Ok Keenan , let's perform an example on the function you mensioned. Let's caclculate 1st & 2nd ... | |
| calculus, Illumination problem | 11/19/2008 |
| Q: Class: Calculus-1000 Consider a horizontal road illuminated by two lights, where Pi is the ... A: We suppose that both light sources gives a a lightening brightness or clarity of ... | |
| Calculus | 11/17/2008 |
| Q: A box with a square base and open top must have a volume of 32,000 cm cubed. Find the dimensions of ... A: Let's suppose that a point(xo,yo) lies on the ellipse curve. & it is the vertex or the rectangle ... | |
| continuous function | 11/17/2008 |
| Q: I have function f(x) which is continuous and nonnegative. Is it possible to show (to prove) that: ... A: For every continuous nonnegative function f(x), in the interval [a,b], always max{f(x)} ≥ ... | |
| Calculus | 11/17/2008 |
| Q: A box with a square base and open top must have a volume of 32,000 cm cubed. Find the dimensions of ... A: The volume of this box is x*x*y , where x is the length of the square base & y is the height. So, ... | |
| Antiderivative? | 11/17/2008 |
| Q: A particle is moving with the given data. Find the position of the particle. a(t) = t2 - 4t + 8 s(0) ... A: The acceleration is a(t)=t^2-4t+8, to find the position equation we must integrate twice : ("1st ... | |
| I don't get it | 11/17/2008 |
| Q: xsiny-ysinx = pi a) find dy/dx b) find equation of tangent line at (pi/2,pi) A: We need to remember that in deriving implicit functions : 1. d/dx {x} = 1 2. d/dy {y} = y' 3. ... | |
| So confused | 11/17/2008 |
| Q: f(x)= -ln(x-3) a) find the inverse function of f^-1(x) b) graph f and f^-1 on same axes and draw any ... A: a) To find inverse function , we switch positions of x & y : x=-Ln(y-3) -> -x=Ln(y-3) -> ... | |
| AP Calculus BC | 11/16/2008 |
| Q: cONSIDER THE CURVE GIVEN BY X^2+4Y=7+3XY (A)show that dy/dx=3y-2x/8y-3x (B)show that there is a ... A: 1st of all I think you have a mistake , instead of 4y it should be 4y^2. So, (A) ... | |
| calculus 3! | 11/15/2008 |
| Q: A particle moves in space along a curve with representation r(t)=t(i)+2sin(t)j+3cos(t)k for ... A: Our 3D trajectory is r(t)=t [i] + 2sin(t) [j] + 3cos(t) [k]. A. To find velocity we need to derive ... | |
| Exponential functions | 11/15/2008 |
| Q: I need help for this a) differentiate (e^x)/(1+e^(-x)), b)find the equation of the tangent to the ... A: a)In this suction we will use 2 rules : 1. (e^x)'=e^x , (e^-x)'=-e^-x 2. (f/g)'=(f'g-g'f)/g^2 So, ... | |
| help | 11/14/2008 |
| Q: "let f(x)=√(1-x),g(x)=x/(x2-1) find fog and domin (f),domain (g) and domain (fog)" f(x)= ... A: The function f(x)=tan(x/3-π) has period of 9π, & here's why : Let's ask our selves when ... | |
| Help on Proof | 11/14/2008 |
| Q: I cam across this problem in one of my math magazines, and I've been on it for days but can't seem ... A: Ok Liz, let's start from the very well know identity : (1+cosx)(1-cosx)=(sinx)^2. (I will leave it ... | |
| calc help please! | 11/13/2008 |
| Q: An object moves in space with acceleration a(t)= t(i)+t^2 (j)+cos(2t)k for t >= 0. If the initial ... A: Ok Sam, We know that the Velocity vector is the integration of the acceleration vector, so : ... | |
| Optimization | 11/13/2008 |
| Q: Suppose that you go to a lake on a nice summer day. Someone throws a ball into the water and it ... A: Let's find the optimal rout (shortest possible amount of time) : If you observe the drawing attached ... | |
| plz help me urgent | 11/12/2008 |
| Q: prove that the fuction f(x)=x^3-2x+3 is countinous.. A: Let's follow the ξ-δ proof : Lim f(x) Where x->c means : For every ξ>0, there exists ... | |
| Implicit Differentiation | 11/12/2008 |
| Q: Given: f(x,y)= a constant, Find the derivative dy/dx a.) 1/y + 1/x = 0 A: Ok Alyssa we know that f(x,y)=1/y+1/x & we are interested in diffrentiating the form f(x,y)=a, So ... | |
| rate | 11/11/2008 |
| Q: A ladder 15 feet long is leaning against a building so that end X is on level ground and end Y is ... A: According to Pythagoras : y(t)=√[15^2-x(t)^2]=√[225-x(t)^2]. So ... | |
| Calculus | 11/11/2008 |
| Q: how do i evaluate the limit as x approaches 0 for sqrt(x^2-4) -2 over x^2? A: Two things Samanthta : 1st , what do u mean by over ? is it dividing ? 2nd , note that ... | |
| Dog Curve | 11/10/2008 |
| Q: Here is a problem I can't solve: A dog is standing in "B" point on the "X" axis. It's owner is ... A: Suppose that the owner's velocity is a & the dog's velocity is b. At a given point M(x,y) on the ... | |
| Calculus | 11/10/2008 |
| Q: Water is draining out of a cone shaped tank. V=(1/3)pir^2h. Find the change in volume knowing ... A: Ok Andy, what you did was the right path but you forgot to derive according to the rule : ... | |
| Calculus practice problems | 11/9/2008 |
| Q: I have these practive problems, and I seriously don't understand them at all. Please help! 1. Oil ... A: This a very long exercises & too much. But, I am willing to help you. I want 1st to explain to you ... | |
| Instantaneous rate of change problem | 11/8/2008 |
| Q: 1) A water bucket containing 10 gallons of water develops a leak. The volume v of water in the ... A: Ok, so we know the following : V(t)=10(1-t/100)^2 (" The volume of water remaing in the tank"). ... | |
| derivatives | 11/8/2008 |
| Q: Can you help me derive (y-2x)/(2y-x) I know the answer is -6/(2y-x)^3 help? A: to derive {(y-2x)/(2y-x)} we must keep in mind that : d/dx {x} =1 d/dx {y} =y' d/dx {f/g} = ... | |
| velocity, speed word problem | 11/8/2008 |
| Q: 1) A ball thrown vertically upward at t=0 seconds has an initial velocity of 96ft/sec and initial ... A: Suppose that g=32 ft/s^2. So : a) let's calculate 1st the time till the ball reaches it's max height ... | |
| Equation of tangent line | 11/7/2008 |
| Q: Find the equation of the tangent line to the graph f(x)= (x^3+2x-4)(2x^2-(6/x)) at x=2. Looking ... A: The tangent line is a strait line from the form : y=ax+b. So we need to calculate a & b. 1st let's ... | |
| Volume of rotation around a slant | 11/5/2008 |
| Q: I know how to find the volume of rotation of a bounded area if it is rotated around the x or y-axis, ... A: I sent the question to the question pool, but I see that no 1 solved it, so I decided to do so. I ... | |
| Calculus 1 | 11/4/2008 |
| Q: an object is thrown upwards from the ground w/an initial velocity of 128 ft/sec use: ... A: Let's use the position or height function : S(t)=so+vot+(1/2)at^2. In our case so=0 because the ... | |
| AP Calculus | 11/3/2008 |
| Q: What is the f"(x) of f(x)=(2x-5)/(x^2-4) A: f(x)=(2x-5)/(x^2-4) To derive the function we will follow the rule : [f/g]'=[f'g-g'f]/g^2 ... | |
| Calculus | 11/3/2008 |
| Q: If y^2 = 1 + (2/x), find (d2y/dx2) in terms of y and x. If f(x)= 4x-(1/x), x>0, and g is the ... A: 1) y^2=1+2/x d/dx { y^2=1+2/x } : 2yy'=-2/x^2 d/dx { d/dx { y^2=1+2/x } } = d/dx { 2yy'=-2/x^2 } : ... | |
| Relative max/min | 11/3/2008 |
| Q: I was given y=x(sqrt(3-x)), and I need to find the relative max and min. I found the first ... A: Hey Molly, let's review some facts about derivating square roots : 1. [√x]'=1/2√x 2. ... | |
| calculus problem help | 11/3/2008 |
| Q: A rectangular page is to contain 24 square inches of print. The margins at the top and the bottom of ... A: Let's set the dimensions as x & y. The area of the paper is xy & it is equal to 24. The effective ... | |
| Calculus problem | 11/2/2008 |
| Q: Trying to find 2nd derivative of 4x^2 + y^3 = 2x + 7y at (-1, 2) 1st derivative ... A: Let's derive with respect to x : d/dx { 4x^2+y^3=2x+ 7y } = 8x+3y^2*y'=2+7y' -> y'(7-3y^2)=8x-2 -> ... | |
| integration | 10/31/2008 |
| Q: I am stuck on the following integral: sqrt(a - bx^2)dx Actually, i need to solve the following ... A: Ok, the answer is : ... | |
| calculus | 10/29/2008 |
| Q: Find the derivative of y= sin^2 (4x) cos (3x) with respect to x A: Here are the rules that we will use to solve the problem : 1. (fg)'=f'g+fg' 2. sin^2(ax)'=2a*cos(ax) ... | |
| L'Hospital's Rule | 10/26/2008 |
| Q: Find the following limits: a. lim x->Infinity ((lnx)^3)/x^2 b. lim x->0 (cosx)^(1/x^2) A: a. applying L'Hospital rule we get : 3(lnx)^2*(1/x) (6lnx) ------------- = --------- 2x ... | |
| Related Rates | 10/26/2008 |
| Q: Both the radius and the height of a circular cone change at the rate of 2 cm/s. How fast is the ... A: The volume of the con is : (1/3)*pi*r^2*h. Weknow that : h(t)=2t & r(t)=2t. So, ... | |
| Number | 10/26/2008 |
| Q: What does number range from. I know it starts form 0 to infinity. What is infinity? When it say ... A: 1st of all Numerable numbers are the group of Normal numbers that we know : 1,2,3,4,5,6 .... .This ... | |
| Integration | 10/25/2008 |
| Q: I am having difficulty integrating an equation. I will provide the work I have done on it thus far, ... A: Ok Kaela, let's start from what you did : ∫arcsin(x)dx=? If we assume that u=arcsin(x) then ... | |
| Integration | 10/25/2008 |
| Q: How to integrate 1.2v/(1+3v^2)dv 2.1/srt(1+v^2)dv A: 1. ∫2v/(1+3v^2) dv = (1/3)∫6v/(1+3v^2) dv = (1/3)∫[1+3v^2]'/(1+3v^2) dv = ... | |
| Related Rates of a Cone | 10/24/2008 |
| Q: Water is leaking out of an inverted conical tank at a rate of 10,000 cm/min. The tank has a height ... A: Ok William ,let's define some variable based on the drawing in the attachment : R=4m (" The ... | |
| limits and rationalizing | 10/23/2008 |
| Q: can you help me with this problem? If h(x)=(squareroot of x+9) + 3/ x.... Show the lim h(x) does ... A: If I understood correctly , then √(x+9) + 3 h(x) = --------------- x We ... | |
| Derivative | 10/21/2008 |
| Q: How would I find the derivative of this..... (58+Rpi)(500000/pi)(r^-1)+)19*pi*r^2) where R is a ... A: d/dr { (58+πR)(500000/π)r^(-1)+19πr^2 } = (58+πR)(500000/π) * d/dr { r^(-1) ... | |
| double integral, cardioid | 10/20/2008 |
| Q: Let R be the region in the xy-plane above the x-axis, bounded by the cardioid r=2+Cos(theta) a. ... A: Ok Heather, we have to integrate above the region R. But, since the region is given in polar ... | |
| derivatives | 10/18/2008 |
| Q: I'm kind of confused... I need help finding the derivative for f (x) = ln ((x2√4x + 1) / (x3 ... A: Ok Marie , this function f(x)=ln[x^2√4x+1]/(x^3 + 5)^3 is composed of multiply & division of ... | |
| Differential equation | 10/18/2008 |
| Q: Find the particular solution to the differential equation y′ = 3y given the general solution ... A: This differential equation is homogeneous 1st order. & the particular solution is ce^3x. We need to ... | |
| Calculus-2 help- trigonometric integrals under principles of integral evaluation chapter | 10/18/2008 |
| Q: Good evening, sir. I have trouble solving this three problems. 1. Rewrite sin x + cos x in the form ... A: Ok Nayan, 1st of all let's write sin(x)+cos(x) as Asin(x+Ø). You must agree that ... | |
| evaluating integrals | 10/18/2008 |
| Q: Evaluate the integral: ∫((x2 + x + 1) / (x2 + 1)) A: Ok Casy, notice that ∫((x^2+x+1)/(x^2+1))=∫((x^2+1)/(x^2+1))+∫x/(x^2+1)= ... | |
| calculus max/min problems | 10/17/2008 |
| Q: There are 2 problems that i can not seem to figure out. 1. Find the dimensions of the rectangle of ... A: 1. As Its drawn in the image I attached, we conclude that : y=(a^2-x^2)^(1/2). The area of the ... | |
| a optimization problem | 10/16/2008 |
| Q: 1) According to the South Coast Air Quality Management District, the level of nitrogen dioxide, a ... A: Ok, our target function is A(t)=t^3(t-7)^4+2018 . Let's derive it & set the derivative equal to ... | |
| optimaization problems | 10/16/2008 |
| Q: i am having trouble with this optimization problem. 1)a closed rectangular box is to be constructed ... A: Let's consider the dimensions of the box as follow : x is the width of the base , 2x is the length ... | |
| Math | 10/16/2008 |
| Q: Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set a) A ∩ B b) A ... A: a) {3} ("the common elements") b) {3} ("the common elements") c) {1,2,3,5,7} ("combining both ... | |
| Related Rates | 10/16/2008 |
| Q: A water tank that is in the shape of a sphere has a radius of 4 meters. When the tank is filled to a ... A: Ok Joanna, 1st of all we know that the volume of speher is ... | |
| Linear vs. Angular Speed | 10/16/2008 |
| Q: a patrol car is parked 50 feet from a long warehouse. the revolving light on top of the car turns ... A: The rate of revolving is 30, which means θ=180t where t is in sec. Let's set x as the distance ... | |
| Derivatives (dA/dd & dA/dC | 10/15/2008 |
| Q: Here is myRate of Change of the Area of a circle with respect to a) diameter b) circumference A: As we know the area of the circle is : A=πr^2. We know that d=2r ("d is the diameter") So ... | |
| MATH 1520 Calculus for Management and Social Sciences | 10/15/2008 |
| Q: I'm struggling with grasping on how to get the answer to this question. The book shows no examples ... A: I Didn't understand if the function that you wrote is 5+x or (5+x)/x(x-2), but I will solve for both ... | |
| Independent Value Theroem | 10/15/2008 |
| Q: I just need help understandong it Using the IVT find an interval on which the function y=x^3+5x-2 ... A: The x-intersection will happen when y=0. & because the function is continues, that means that ... | |
| Calculus limits | 10/15/2008 |
| Q: I understand limits perfectly I m a genious at math, but how to find limits on absolute values ... A: Whenever there is absolute, it means there is a shift of sign. So the trick here is to know that : ... | |
| hai | 10/15/2008 |
| Q: evaluate integral x^3/sqrt(x^2+1) dx A: let's use the substitue methods : Let u=√(x^2+1) . (Where "√" resimble square root), ... | |
| Calculus | 10/15/2008 |
| Q: A lot has the form of a right triangle,with perpendicular sides 60 & 80 ft long.Find the length and ... A: Ok, let's solve it : 1st : x/(60-b)=80/100 --> 100x=4800-80b --> b=60-(5/4)x 2nd : b/y=60/100 --> ... | |
| calculuse | 10/15/2008 |
| Q: good morning . can you help me please in solving the following equation : sin (2x ) + tan ( x ) = ... A: Let's use the trigonometrical identity : sin(2x)=tan(x)/[1+tan^2(x)] We get : ... | |
| Velocity and Rate of Change (Calculus) | 10/14/2008 |
| Q: The position (x-coordinate) of a particle moving on the line y = 2 is given by x(t) = 2t^3 -13t^2 + ... A: The particle is moving in a straight line, with increase & decrease in it's velocity. When x'(t)=0 ... | |
| Calculus | 10/13/2008 |
| Q: A lot has the form of a right triangle,with perpendicular sides 60 & 80 ft long.Find the length and ... A: From the drawing that sent you, you can conclude that : 1. y=(a^2+b^2)^(1/2) 2. a/y=x/(60-b) 3. ... | |
| Maximize | 10/11/2008 |
| Q: I hope its okay if I ask about another. My problem on the optimization problems is that I always ... A: Ok Gracie, let's make it simple : Let's 1st see how much bushels the farmer will have every week : ... | |
| calculus | 10/11/2008 |
| Q: The question is Y^(3/4) = 2x+2. I would like to solve for Y (Leave Y by itself on the left hand ... A: In these kind of cases Y(x) can be achieved by befroming power of (4/3) for both sides, which mean ... | |
| Optimization Problem | 10/10/2008 |
| Q: A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass ... A: Ok, let's set x & y are the dimensions of the fence. Then the perimeter of the rectangular fencing ... | |
| Vector Functions | 10/9/2008 |
| Q: I have some homework problems that are being graded as a quiz in my Calculus 3 class. There is one ... A: Ok, in this case our space trajectory or our 3D curve will be : ... | |
| Vector Functions | 10/9/2008 |
| Q: I have some homework problems that are being graded as a quiz in my Calculus 3 class. There is one ... A: I quote what you wrote to me : " the radius is 10 angstroms, rises 34 angstroms for each complete ... | |
| Vector Functions | 10/9/2008 |
| Q: I have some homework problems that are being graded as a quiz in my Calculus 3 class. There is one ... A: The shape of the DNA is 3D spiral . Where the radius grows in fashion of ... | |
| Calculus Derivatives | 10/8/2008 |
| Q: I need to know how to solve the following derivative: lim sqrt(x-1) h->0 A: So, you are interested in calculating the derivative of sqrt(x-1). Ok, let's use the definition: ... | |
| tangents | 10/8/2008 |
| Q: find the equation of the line that is tangent to y=x^2-(5x^1/2)-10 at x=4 A: The equation of the line that is tangent to y=x^2-(5x^1/2)-10 is of the form : mx+n -> where m=f'(x) ... | |
| differentiation | 10/5/2008 |
| Q: 1. Suppose variables x and y are related by: xy+2sin(y^2+1)=sin(x^2y^2) Find an expression in ... A: Sarah, what you calculated concerning h'(t) is not correct at all : If h(t)=sin(2t^2-6) then ... | |
| Math | 10/4/2008 |
| Q: Two villages, Abu and Bip, lie at distances 2km and 1km above a river. River is 4km long.It has ... A: Let's set x the distance from Abu to the station, then 4-x is the distance from Bip to the station. ... | |
| Integrate Problem | 10/4/2008 |
| Q: I'm trying to Integrate 4x + 5 divided by sqrt 2x - 3 and have been given 2x - 3 = t^2 as the ... A: If you use the substitution t=2x-3 then dx=dt/2. & the integral becomes : ... | |
| Equation of Tangent Line | 10/3/2008 |
| Q: x^2 + xy + y^2 = 1 a) find all pts which the tangent line is horizontal (m=0) b) find all pts in ... A: The best way is to write y as function of x : x^2 + xy + y^2 = 1 --> y^2+y*x+(x^-1)=0 --> ... | |
| related rate question | 9/30/2008 |
| Q: could you help me with this related rate problem? a horizontal cylindrical oil tank (the length is ... A: Ok, first of all let's find a relation between w & h . From simple geometry & Pythagoras theorem you ... | |
| Related Rates | 9/30/2008 |
| Q: A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast ... A: Let's first write the formula of the volume of the spherical balloon V=(4/3)πR^3. This means ... | |
| Math question | 9/29/2008 |
| Q: How to sketch the surface with equation z^2= 2x + 4y^2 A: You may see that z^2= 2x + 4y^2 is not a 3D function but 3D object symmetric along the x-y plane. & ... | |
| Calculus | 9/28/2008 |
| Q: what is the lim as X approaches 0 ln(1-x)-sinx/x ANSWER: The lim of our function is composed of 2 ... A: The area of R is the finite integral of (4-2x)-[x^3/(1+x^2)]. from zero to 1.49. The two graphs ... | |
| Integrals | 9/28/2008 |
| Q: I been working on the integration of X^X do you know a method for it. I tried integration by parts ... A: This integral is associated with the identities of Sophomore's dream There is no former function ... | |
| tangent to a curve | 9/27/2008 |
| Q: my question is: if the equation of a curve is y=x-sin x cos x; find the equation of the tangent to ... A: Ok, whenever π is outside a cos or sine function , it's values is 4.1315, & when its inside a ... | |
| Limit Dilemma | 9/25/2008 |
| Q: I have a limit that looks as such: lim x -> -3 (x^2-x+12) / (x+3). 1. When I sub in the -3 for x, I ... A: Well Stephanie , as you can see the function (x^2-x-12)/(x+3) has singularity in x=-3. Singularity ... | |
| derivatives | 9/25/2008 |
| Q: if x^2 -y^2 = 1, find the second derivative at the value (2, square root of 3) A: Ok Kristin , finding derivative of Implicit functions can be done in 2 ways : 1st way : x^2-y^2=1 ... | |
| Tangent lines | 9/25/2008 |
| Q: Find the lines that are (a) tangent and (b) perpendicular to the curve at the given point. ... A: Let's refresh our memory : Tangent line is a line that is parallel to x-axis, & its calculated at ... | |
| Discontinuous functions | 9/24/2008 |
| Q: I'm having trouble with some specifics of this problem. I think I understand the idea of continuity ... A: Ok Lindsey, you can notice that the function (x^2-2x-8)/(x-4) has singularity at x=4. Singularity ... | |
| physics+Math | 9/24/2008 |
| Q: what is the lim as X approaches 0 ln(1-x)-sinx/x A: The lim of our function is composed of 2 forms : ln(1-x) & sinx/x. Now, well known that Lim x->0 ... | |
| calculus help, please? | 9/24/2008 |
| Q: AP Calculus would be a lot more fun if i knew what the hell i was doing. Can you help me out of this ... A: The horizontal tangents are the lines that parallel to the x-axis. That means that the slope of ... | |
| limit with square roots | 9/22/2008 |
| Q: I need to know how to solve the following limit: lim as x->0 square root (2-t) + square root of (2) ... A: Let's define SR(a) as square root (a). So if you meant : Lim{t->0} [ SR(2-t)+SR(2) ]/t Then the ... | |
| Integrate | 9/21/2008 |
| Q: I am trying to integrate (e^x - 1 )^2 with definite limits 1 (at top ) and -1 (at bottom). I ... A: Ok Carole, the first think we will do is deal with the power : We know that (a+b)^2=a^2-2ab+b^2, so ... | |
| Derivatives | 9/21/2008 |
| Q: I am working on the Derivatives with the COW tutorial and I need help, please, on the following ... A: The function is f(x)=x^2 & the slope is -2. That's intuitive, because f'(x)=2x & f'(-1)=-2. But ... | |
| limits | 9/18/2008 |
| Q: I'm having truble solving this problem f(x)=|25x^2-16| it asks to find the points in which the ... A: Ok Anna, the function f(x)=|25x^2-16| is defined : f(x)=25x^2-61 if 25x^2-16>0 & -25x^2+16 if ... | |
| composite rule | 9/17/2008 |
| Q: use the composite rule to differentiate the function f(x) = √10+ x^2 i'm totally lost.can you ... A: Ok Soraia, let's set u=10+ x^2, then u'=2x. We know that (√u)'=1/(2√u). So now we can ... | |
| precalculus | 9/16/2008 |
| Q: an open box is to be constructed from a rectangular piece of sheet metal 8 by 12 inches by cutting ... A: Ok, let's consider the cut of corners : The area of the cut corners is in a shape of isosceles ... | |
| rotating about an axis and finding the area | 9/14/2008 |
| Q: Find the area of the surface obtained by rotating the curve about the x-axis. y = x^3 0 ≤ x ... A: let's solve this exercise step by step, shall we? OK, 1st let's write the formula of surface area of ... | |
| maths | 9/14/2008 |
| Q: We know area of BCD = 200 sin 2x. Can we find an expression for BD^2 and can we use this to show ... A: First of all , yes we can express BD^2 as function of x, for that we can use 2 methods : 1. Cosine ... | |
| calc question | 9/13/2008 |
| Q: what is the limit of sinx/x as x approaches pi/2? A: Cassie , the point x=pi/2 is not a singularity for the function sin/x, the function is well defined ... | |
| maths | 9/13/2008 |
| Q: A sector of a circle is 16cm^2 Show the perimeter of sector is 2(r + 16/r ) A: The perimeter of the sector is : r+L+r, where L is the length of the arc. In order to find it , we ... | |
| Discontinuity | 9/11/2008 |
| Q: Determine where the function g(x) has discontinuity. Label the type of discontinuity and if ... A: If you set the value x=0 in the function you will get 0/0 which is unknown, so we have singularity ... | |
| Limits and Polynomials | 9/11/2008 |
| Q: Find examples of polynomials p(x)and q (x) such that lim(x->infinity) p(x) = infinity and ... A: Ok, Kristin , we have the condition : p,q->INF when x->INF that mean they are diverging functions. ... | |
| Vertical and Horizontal asymptotes | 9/11/2008 |
| Q: Given the function y = (x-b)/ (2x^2 - 2b^2), find all vertical and horizontal asymptotes. if there ... A: Kristin notice that (x-b)/(2x^2 - 2b^2)=(x-b)/2(x^2-b^2)= =(x-b)/2(x-b)(x+b)=1/2(x+b). & this ... | |
| Calculus | 9/10/2008 |
| Q: In my college class we have two questions to correct for homework and i can't figure it out to save ... A: Ok Ashleigh , these 2 limits can be calculate analytically, & that's what I'm going to show you ... | |
| how to prove does not exists linlit by definition of limit? | 9/7/2008 |
| Q: Let F(x)={0, if x is irrational 2, if x is rational Use definition of limit to prove that ... A: The definition of limit is Lim x->a+ = Lim x->a- = Lim x->a. Where a+ represent approaching a from ... | |
| calculus-arc length | 9/7/2008 |
| Q: please could you help me find the arc length of this curve:x=(y^3/2 -3)-y^1/2...from y=1 to ... A: So, our function is x(y)=y^(3/2)-3-y^(1/2). In this case the arc length is defined by : ... | |
| limit | 9/7/2008 |
| Q: I have another question, please. My C.O.W. Tutorial treats 1 and 2 below as two different ... A: Indeed, what you said was true, you will get the same result either by plugging the value 2 , or ... | |
| Calculus Limits Questions | 9/5/2008 |
| Q: How do I evaluate these problems? (a) lim x->3 ln(3-x) (b) lim x->4+ ln(x-3) A: we are going to solve this kind of question in a little bit different way. Now, we all know that if ... | |
| Triple integral | 9/3/2008 |
| Q: It ask to setup the triple integral that represent the volume of a tetrahedron that is enclosed by ... A: The chain rule of partial derivative is df/dr=(df/dx)(dx/dr)+(df/dy)(dy/dr)+(df/dz)(dz/dr), the ... | |
| Triple integral | 9/2/2008 |
| Q: It ask to setup the triple integral that represent the volume of a tetrahedron that is enclosed by ... A: The volume of the three-dimensional region E is given by the integral ... | |
| calculus | 9/1/2008 |
| Q: I am learning Calculus from the C.O.W on-line tutorial, just for fun and as a personal challenge , ... A: The expression A+(h)times epsilon in our case is : 0+h^3-6h^2+9h . Since h^3-6h^2+9h is vanishingly ... | |
| calculus | 8/31/2008 |
| Q: I am learning Calculus from the C.O.W on-line tutorial, just for fun and as a personal challenge , ... A: the math rule for the binom of third form is : (a+b)^3=a^3+3a^2b+3ab^2+b^3. I think you have been ... | |
| calculus | 8/30/2008 |
| Q: what will be the derivatives of these functions? a) r=sin(3(pi)t/2+cos(3(pi)t/2, ... A: I think that you are ready to start calculating derivatives, I will help you through those by giving ... | |
| derivative | 8/30/2008 |
| Q: How do I take the derivative of |Sin(t)| with respect to t(the absolute value of Sin(t) with respect ... A: The function |sin(t)| is defined as follow : |sin(t)|= sin(t) ; if sin(t)>0 & -sin(t) ... | |
| Pre-cal | 8/29/2008 |
| Q: (x2+x-2)(x3-x+1) A: Did you mean (x^2+x-2)(x^3-x+1)=? , If yes then let's start multiplying each element, according to ... | |
| precalulus homework help | 8/29/2008 |
| Q: a closed box has a base twice as long as it is wide. if its volume is 100 cubic inches, express its ... A: A box is compounded from 6 plains : 1. 2 bases (up & down), we will call them B1 & B2 2. 2 side ... | |
| precal | 8/29/2008 |
| Q: a cylindrical container with a circular base has a surface area of 64 square feet. express its ... A: The volume of the cylindrical container = A*h , where A is the area of the base, & h is the height. ... | |
| calculus | 8/27/2008 |
| Q: what will be the derivatives of these functions?a) y=(4x+3)^4(x+1)^-3 ... A: a) y=[(4x+3)^4]*[(x+1)^(-3)]. Applying the rule of (fg)'=f'g+fg' : ... | |
| advanced calculus proof of paralellogram law | 8/27/2008 |
| Q: I need to show that: ||x -y||||x +y|| ≤ ||x||² +||y||² can you show me how to do this? I'm ... A: I moved your question to the question pool, but I sow that no one solved it, so I decided to do that ... | |
| calculus | 8/26/2008 |
| Q: what are the derivatives of these functions a)h(x)=xtan(2*underrootx)+7, ... A: Let's start with the 1st function : H(x)=7+x*tan[2*sqrt(x)] ... | |
| newton's law of cooling | 8/25/2008 |
| Q: in newton's law of cooling [ dT/dt = -k (T-Ts) ]: what does 1/k represent? [k being the constant in ... A: k is a positive constant of proportionality that depends on the material properties of the ... | |
| Asymptote | 8/24/2008 |
| Q: We have been teached to find the asymptotes of polar curve by using formula- Rsin(Theta -alpha ... A: The formula of the asymptotic line is : g'(Ø) r = ---------- sin(Ø - Øo) Where ... | |
| solve for indicated variable (pre-cal) | 8/23/2008 |
| Q: h=1/2gt^2 + v0t solve for t A: this is a quadratic equation. Let's change a little bit how its written : h=1/2gt^2 + v0t = ... | |
| Pre-Cal | 8/23/2008 |
| Q: (t-4)^2 = (t+4)^2 + 32. solve the equation A: Ok Ashlee, for this kind of equation, we will use a very nice trick. a trick which is a rule ... | |
| gaussian elimination method | 8/23/2008 |
| Q: ! I'm trying to solve this system of equations using the Gaussian elimination method. can you help ... A: Ok, let's call the 1st row R1, the 2nd R2 & the 3rd R3. Now we have the matrix : 1 4 -1 9 ... | |
| simplifying fractions where with x (x is to the power of -1 or less) | 8/22/2008 |
| Q: i have two problems i have no idea what to do on, and i realy dont know what to call them, i do know ... A: Ok, the majour rules that we will use when simplifying is : 1. a^2-b^2=(a-b)*(a+b) a/b a 2. ... | |
| calculus | 8/18/2008 |
| Q: A horozontal trough is 16 meters long, and its ends are isosceles trapezoids with an altitude of 4 ... A: OK, we will solve this question step by step. First let's review some of the facts & define some ... | |
| integration | 8/17/2008 |
| Q: pleez help me to integrate 1/1 +cos x.tnx A: OK, if I understood right , The Integrand function is : 1/[1+cos(x)tang(x)]=1/[1+sin(x)], so our ... | |
| Calculus, Functions of several variables | 8/12/2008 |
| Q: I am trying to investigate stopping distances as related to tailgating. Beginning drivers are often ... A: Certainly not ! d(2v) Not Equal 2d(v). In order to understand the relationship between the distance ... | |
| Calculus derivative | 8/11/2008 |
| Q: Find dy/dx for y = x arc cos 2x A: Finding derivatives of such kind, involves inversion : If y=x*arc[cos(2x)] then ... | |
| doubling money | 8/7/2008 |
| Q: Doubling ur money: determine how much time is required for an investment to double in value if ... A: The formula for such future value is : Fv=P(1+r)^n where, Fv is the future value of the investment,r ... | |
| Calculus | 8/6/2008 |
| Q: Can you also help me with this one? Find the length of the curve y=(2/3)x^(3/2) , 0≤x≤3 A: the formula of arc length is : s=∫sqrt[1+f'(x)^2]dx. Let's calculate the derivative of f(x) ... | |
| Calculus | 8/6/2008 |
| Q: I need help Find the volume of the solid obtained when the region bounded by the curves y=2x-x^2 ... A: We will use the 'shell' method : V=2π∫xf(x)dx. Our region is composed of two semitric ... | |
| Differentiation | 8/5/2008 |
| Q: Looking for the solution to d/dx ln((x^2+y^2)^(1/2))/a Can you help? A: If y is independent of x then dy/dx=0.If not then dy/dx=y' {Ln[f(x)]}'=[1/f(x,y)]*[df(x,y)/dx]. ... | |
| Calculus | 8/5/2008 |
| Q: Please solve F(x) = (6x + 12)^2/3 for relative min and max A: The function F(x) doesn't any extermum points. The derivative is monotonic & continues & never ... | |
| functionns their domain,range | 8/4/2008 |
| Q: f(x)=xpower2 -4x for x<2 and f(x)=x-4 for xgreater or equal to 2.g(x)=x-3 for x <3 and ... A: f+g = h 1. for x<2 h(x)=x^2-3x-3 2. for 3≤x (greater or equal) h(x)=x^2+3x-2 3. for ... | |
| thread length | 7/31/2008 |
| Q: I want to know the thread lenght if it is wound on a cylinder at a certain pitch. eg. cylinder 50mm ... A: Let's make parametrization to our thread Lulianic curve : x(t)=25cos(t) y(t)=25sin(t) z(t)=12t , ... | |
| related rates equations | 7/30/2008 |
| Q: The apparent temperature A in degrees F is related to the actual temperature x and the humidity ... A: As you can see in the link below, the apparent temperature is a surface (2D function), which it's ... | |
| calculus | 7/28/2008 |
| Q: 1. Find the equation of the normal to the curve y = 2x / x^2 + 1 at the point (3;0,6) and the ... A: 1. Let's start with the tangent : The tangent line has slope of 'derivative' of the function in ... | |
| sqeeze theorem | 7/23/2008 |
| Q: how can i prove this squeeze theorem? lim sin t x approaches 0 ______=1 ... A: we will prove it in 3 different ways: 1) Lopital's low Lim [f(x)/g(x)] = Lim [f’(x)/g’(x)] Lim ... | |
| Derivative of arc length | 7/21/2008 |
| Q: I had asked this question originally on the site:www.thestudentroom.co.uk But,I couldnot understand ... A: Sorry, still didn't get any link. Any way, I'll try to build the missing details, I just have 2 ... | |
| Derivative of arc length | 7/21/2008 |
| Q: I had asked this question originally on the site:www.thestudentroom.co.uk But,I couldnot understand ... A: I'm sorry, but I was asked to enter user name & password. So I couldn't see the picture of the ... | |
| Integration | 7/21/2008 |
| Q: How do you evaluate this definite Integral : Integral of (x^2)*e^(-x^2) with limits from 0 to 1? I ... A: If you set u=x^2 the integrand becomes (1/2)*[sqrt(u)e^-u]. From the table of integrals you find : ... | |
| need help | 7/17/2008 |
| Q: can uyou please tell me what is the integration of square of <dx> A: I'm not quite sure that I understood what you meant, but here's my answer : dx is the infinitesimal ... | |
| cal 1 | 7/16/2008 |
| Q: a card board box of 32 inches cube in volume with a square base and open top is to be constructed. ... A: Set x as the length or width of the base. We know that the volume is 32 so the height h=32/x^2 ... | |
| calculus | 7/15/2008 |
| Q: What is the formula to calculate the slope of plane? A: The equation of a line in 2 dimension is ax+by=c, where -b/a is the slope, or the tangent(of the ... | |
| limit question | 7/11/2008 |
| Q: I have a question similar to lim x approaches infinity of e^-x times e^x. It seems to me that the ... A: Ok, our function is e^(-xe^x). Let's get started first by intuition: e^(-xe^x) can be written as ... | |
| Log functions | 6/13/2008 |
| Q: hey Chris i need some help with a problem i need to find f' and state the domains of f and f' for ... A: Let's calculate the derivative of f(x)=Ln(Ln(Lnx)) : As we know, Ln(g(x))'=g'(x)/g(x). So ... | |
| Calculus Maxima and Minima | 6/12/2008 |
| Q: Given y=2x-tanx, 0_<x_<2pi, determine the position of maxima and minima A: First let's find the derivative of y & set it equal to zero : y'=2-1/[cos(x)]^2. (because ... | |
Calculus
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