| Subject | Date Asked |
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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). ...
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| 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 ...
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| 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, ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 --> ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 & ...
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| 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 ...
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| 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)] --> ...
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| 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 ...
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| 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 ...
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| 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 . ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 : ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 , ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 : ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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), ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 , ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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) = ...
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| 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 ...
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| 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 ...
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| 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)= ...
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| 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 ...
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| 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) * ...
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| 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) + ...
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| 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 ...
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| 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 : ...
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| 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' ...
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| 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 ...
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| 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 ] ...
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| 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 ...
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| 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 ...
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| 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' : ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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' = ...
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| 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 : ...
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| 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 * ...
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| 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 ...
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| 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 = ...
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| 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 ...
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| 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) ...
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| 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 ...
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| 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 ...
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| 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)] } '= ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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/{ ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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) ]' = ...
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| 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 ...
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| 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) ...
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| 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. ...
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| 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 ...
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| 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). ...
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| 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" ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 = ...
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| 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 ...
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| 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. ...
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| 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 : ...
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| 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 +...+ ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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) -- = ...
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| 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!! ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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)] ...
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| 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 ...
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| 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) + ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 & ...
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| 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 ...
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| 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) = ...
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| 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 ...
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| 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 -> ...
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| 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] . ...
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| 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 ...
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| 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) ...
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| 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 - ...
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| 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 ...
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| 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 ...
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| 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]. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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} ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 . ...
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| 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 & ...
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| 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) + ...
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| 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) = ...
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| 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) . ...
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| 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) ...
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| 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 ...
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| 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 { ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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- ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 -> ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 & ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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). ...
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| 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 = ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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, & ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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. ------------------------------------------------- ...
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| 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. ...
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| 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 ...
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| 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. ...
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| 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, ...
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| 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 : ...
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| 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 ...
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| 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) + ...
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| 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 ...
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| 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} = ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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; ...
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| 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 ...
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| 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' ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| ? | 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 -> ...
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| 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 & ...
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| 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 : ...
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| 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, ...
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| 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) ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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. ...
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| 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, ...
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| 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 ...
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| 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. ...
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| 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. ...
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| 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 ...
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| 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. ...
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| 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} = ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ∫ ...
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| 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 ...
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| 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. ...
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| 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, ...
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| 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] = ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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) ...
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| 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 ...
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| 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 : ...
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| 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. ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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}|= ...
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| 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 ∞ ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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)} ≥ ...
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| 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, ...
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| 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 ...
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| 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. ...
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| 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) -> ...
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| 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) ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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"). ...
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| 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} = ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 } : ...
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| 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. ...
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| 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 ...
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| 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 -> ...
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| 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 : ...
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| 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) ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 = ...
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| 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 ...
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| 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 ...
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| 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) ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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)= ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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), ...
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| 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 --> ...
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| 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 : ...
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| 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 ...
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| 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. ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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: ...
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| 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) ...
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| 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 ...
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| 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. ...
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| 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 : ...
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| 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 --> ...
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| 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 ...
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| 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 ...
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| 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. & ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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) ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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' : ...
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| 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 ...
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| 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)] ...
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| 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 ...
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| 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 ...
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| 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 = ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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) ...
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| 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 ...
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| 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]. ...
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| 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 ...
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| 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 ...
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| 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 , ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 : ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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