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Calculus/Questions Answered by Expert Abe Mantell
| Subject | Date Asked |
| Calculus - Comparing Related Rates | 1/4/2012 |
| Q: Part of a circuit has two resistors connected in parallel. R1 is a constant resistor of 10 ohm, ... A: In this case, I would solve for R in terms of R1 and R2, then differentiate with respect to t. ... | |
| integral calculus | 8/18/2011 |
| Q: show the circumference of the circle of radius 'r' is 2*pi*r by integration A: Using the formula for arclength: integral sqrt(1+[f'(x)]^2), x from a to b, where f(x)=sqrt(r^2-x^2) ... | |
| Mathematical and Physical Constants | 8/17/2011 |
| Q: Referring to the Wikipedia Link for Mathematical Constants ... A: I would not add g to the list of mathematical constants. A mathematical constant IS CONSTANT ... | |
| Induction proof | 8/14/2011 |
| Q: 1. Prove the formula: 0(2)^0 + 1(2)^1 + ... + n(2)^n = (n-1)[2^(n+1)] + 2 for all integers n>=0 ... A: 1. Proof by Induction: sum(k*2^k, k from 0 to n) I. Show true for n=0 .. 0*2^0=0 and ... | |
| Calculus | 8/11/2011 |
| Q: I don't understand how to do problems like this: q(t)=B-Ae^-kt I have the notes from class so I ... A: Q(t)=B-Ae^(-kt) is a standard exponential model "t" is the independent variable while A, B, and k ... | |
| Calculus | 8/4/2011 |
| Q: Can you please show me step by step how to find the local maximum and minimum values and period if ... A: Neither function has a period, since neither is periodic - the first is a rational function, the ... | |
| asap | 8/2/2011 |
| Q: a solid cube with edge of 10 cm. will be ccovered with paint 1/2 mm thick. find the approximate ... A: The 6 faces are each 10 by 10 or 100 cm^2. So the paint covering them will have a volume of ... | |
| Calculus | 7/25/2011 |
| Q: If you can please help me and show me step by step on this function y=e^(3*x)-1 what is the ... A: Sure! y=e^(3x)-1 y-intercept occurs when x=0 ==> y=e^0-1=1-1=0...so y-int. is at x=0 x-intercept ... | |
| double integral | 7/22/2011 |
| Q: Evaluate"integral 0 to 2a integra 0 to sq.rt(2ax-x^2) '(x^2)'dx dy" A: First, it should be "dy dx" not "dx dy"... So the inner integral is: integral of x^2 dy from y=0 to ... | |
| Calculus area between two curves | 7/17/2011 |
| Q: I am having difficulties trying to get the value of q. I have look for examples in my book for ... A: The area between the two is given by: Integral[(4-x^2-qx) - x^2, x from x1 to x2], where x1 and x2 ... | |
| rate of change | 7/3/2011 |
| Q: A cubical box with sides of length 15cm is covered with ice of uniform thickness. The ice is melting ... A: Let x=the thickness of the ice formation. Then, the volume of ice is the volume of a cube with sides ... | |
| Derivative of Unit Binormal | 6/7/2011 |
| Q: What is the derivative of Unit Binormal in terms of r(t)> Unit Binormal= r'(t) x r''(t) / ||r'(t) x ... A: Since the derivative of a cross-product follows the usual "product rule" and ||r'(t) x r''(t)|| is ... | |
| integration | 5/30/2011 |
| Q: How to find area of an amoeba like figure ? A: One way is to use a square grid to place over the region, then count the number of squares contained ... | |
| Calculus preperation | 5/29/2011 |
| Q: my question isn't necessarily a homework one, but more of an academic circumstance in need of ... A: My advice is NOT to hurry along! I see waaaaaaaay too many students who try to take short-cuts and ... | |
| Calculus | 1/14/2011 |
| Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 6 ... A: A diagram would be helpful, but tough to include here...so I hope you can follow. Since we cut out ... | |
| Area of a region. | 1/13/2011 |
| Q: My question is: Sketch the region between y = ln(x-1), y=1, y=0 and x- y^4 +1=0 and find the area ... A: I have attached an image of the sketch. We take horizintal "slices" so dA=([x-value on ... | |
| Initial Value Problem | 1/7/2011 |
| Q: Dy/dx = -2 (y-3) y(0)=5 Dy/dx = y sqrt(x) y(0)=1 I am having trouble solving these two ... A: They are both separable. 1. dy/dx=-2(y-3) ==> dy/(y-3)=-2dx, now anti-differentiate both sides ==> ... | |
| Calculus AB | 1/1/2011 |
| Q: Consider the curve defined by the equation y + cosy = x + 1 for 0<=y<=2pi. Write an equation for ... A: We need to find where dy/dx is undefined. Differentiating gives: y'-y'sin(y)=1 ==> y'(1-sin(y))=1 ... | |
| linear algebra | 9/3/2010 |
| Q: 4x1+3x2+2x3-x4=4 5x1+4x2+3x3-x4=4 -2x1-2x2-x3+2x4=-3 11x1+6x2+4x3+x4=11 I think there should be a ... A: It is quite a bit to type out the row reductions, but what I obtained is shown in the attached ... | |
| Washington Monument Souvenirs | 8/28/2010 |
| Q: a manufacturer receives an order for 2000 souvenirs which are to be miniature models of the ... A: Let's look at the ratio of heights. 555 ft vs 4 inches...4 inches is 1/3 of a ft, so we have ... | |
| advanced math | 8/27/2010 |
| Q: the rational numbers are countable many, and the real numbers are uncountable many. how many ... A: The continuum hypothesis states that the cardinality of the rationals, denoted by aleph-null, is ... | |
| optional math | 8/24/2010 |
| Q: The diagonals of parallelogram bisect eachother.Prove by vector method A: Here is one way: Let the intersection pt O of the diagonals be the origin,then a,b,c,d are the ... | |
| Calculus Books | 8/23/2010 |
| Q: I am an undergrad. physics student. I have a bunch of calculus books and they are quite distinct ... A: I am familiar (and have) all three of those texts, and it seems to me that you have a good ... | |
| maths | 8/22/2010 |
| Q: two sides of triangle have length a and b and the angle between them i s 'x'. what value of 'x' will ... A: Two ways to anwer this. 1. common sense: Since the area is (1/2)(base)(height), . if we let one of ... | |
| trig equations | 8/19/2010 |
| Q: Can you please show me how to solve the following problems. 1.) cotxcos^2x=2cotx ... A: 1. cot(x)cos^2(x)=2cot(x) ==> cot(x)cos^2(x)-2cot(x)=0 ==> cot(x)[cos^2(x)-2]=0 ==> cot(x)=0 OR ... | |
| Trigonometry | 8/17/2010 |
| Q: I hope you don't mind that I have another question! Your answer to my last question was really ... A: To make the algebra *look* easier, substitute u=sin(x). So, the "new" problem is 2u^2+u-1=0...now ... | |
| Integral | 8/16/2010 |
| Q: Integrate: 1/((cos^2(x) +4sin(x)-5)*cos(x)) AP BC summer assignment Extra credit A: I hate to simply just do the problem for you, since it is an extra credit problem! However, I will ... | |
| Calculus | 8/15/2010 |
| Q: I am working on my AP Calculus summer assignment that is due Tuesday and am having trouble on one of ... A: Regarding the symmetry of graphs... 1. If replacing "x" with "-x" does not change the equation, . ... | |
| calculus | 8/14/2010 |
| Q: My question is, Bob has a ladder that is 5m long resting agaist the top of a 4m high wall. Bob is 3m ... A: My first thought was, "Why is Bob's wife measuring instead of helping to stop Bob from getting ... | |
| Integral by Parts | 6/12/2010 |
| Q: Please help to solve this. Integral (lnx)^2 dx A: Integration by Parts: INT u dv = uv - INT v du Let u=ln(x)^2 and dv=dx, thus du=2ln(x)/x dx and v=x ... | |
| Calculus | 6/7/2010 |
| Q: A spherical balloon is inflated so that its volume is increasing at the rate of 20 cubic feet per ... A: Since V=(4/3)*pi*r^3, dV/dt=4*pi*r^2*dr/dt So that when dV/dt=20, we get 4*pi*r^2*dr/dt=20 ==> ... | |
| math | 6/6/2010 |
| Q: If you started from a centre point and created a golden spiral based on the Fibbonacci numbers,at ... A: The equation for the Golden Spiral is (in polar form): r=a*e^(b*theta), where b=ln(phi)/(pi/2) with ... | |
| triple integral | 1/6/2010 |
| Q: 1- how can i find the volume by useing a triple integral of the solid enclosed by the paraboloid ... A: 1. I gather you want to do the integral in cylindrical coordinates. Thus, . The integral should ... | |
| Calculus: help please | 1/5/2010 |
| Q: I'm posed with the following problem: let f(x) be the function defined by f(x) = k+12x+3x^2-2x^3 ... A: (a) If f'(x)>0, then f is increasing. Thus, we need to solve for x when f'>0 . f'=12+6x-6x^2>0 ... | |
| Asymptotes | 1/4/2010 |
| Q: the question is f(x)= ln(1-cosx) ... I solved in this way.... ... this function is defined when ... A: Is yourWhat is/are the asymptotes of the function f(x)=ln(1-cos(x))?? Yes, f(x) is defined as long ... | |
| Related Rates | 1/3/2010 |
| Q: A kite is at an altitude of 75 feet and moving horizontally at 12 ft/sec. How fast is the string ... A: Since you let dx/dt=12 ft/sec, then you are letting x=the horizontal distance from the person to the ... | |
| 2 variable minima | 1/1/2010 |
| Q: What is the absolute minima of this x^2/(x-1)^2 +y^2/(y-1)^2 + (1/xy)^2 / (1- (1/xy) )^2? ANSWER: ... A: Letting z(x,y)=x^2/(x-1)^2+y^2/(y-1)^2+1/(x^2*y^2*(1-1/(x*y))^2) the partial derivatives are: ... | |
| problem on testing for differentiability | 12/28/2009 |
| Q: The problem gives two functions with variables. We are supposed to compare the equations and then ... A: Let me just go through the entire problem. So, we first need continuity at x=1, thus: e^a = b Then ... | |
| Trigonometry show part | 8/14/2009 |
| Q: Show that the equation tan(30degree+a) =2tan(60degree-a) can be written in the form (tan^2) a+ ... A: :-) Use the sum and difference formulas for tangent: ... | |
| Calculus | 8/11/2009 |
| Q: Please explain it so I understand The curve y=ax^2 + bx+c passes through the point (1,6). The ... A: Since (1,6) satisfies y=ax^2+bx+c, we get: 6=a+b+c...since the tangent line at x=1 is horizontal, ... | |
| Maximizing Area | 7/21/2009 |
| Q: Given two positive constants a and b. If two sides of a triangle are of length a and b, find the ... A: Since the area of a triangle can be written as: A=(1/2)(a)(b)sin(C), where C is the angle between ... | |
| 3rd Derivative | 7/20/2009 |
| Q: Function f(x) = x^4-3x^2 1st Der f ‘ (x) = 4x^3-6x 2nd Der f ” (x) =12x^2-6 3rd Der f ... A: 1. What is happening to f(x) or f''(x)??? 2. You want to maximize f'''(x)? So, take the derivative ... | |
| calculus | 7/16/2009 |
| Q: 1.State the vertex of x2 – 2x – y = 0. 2.State the equation of the directrix of (y – 4)2 = –8(x ... A: 1. y=x^2-2x has vertex at x=-b/(2a)=2/2=1, so x=1 and y=-1 ==> (1,-1) 2. Basically, if you arrange ... | |
| Differentiablity | 7/15/2009 |
| Q: I'm a guy from India preparing for IIT(Indian Institute of Technology) entrance exams. I have a ... A: It is OK to differentiate the function in question and examine it for any "problem" values, provided ... | |
| Quadratic Formula | 7/14/2009 |
| Q: It has been many years since I have done this type of math. Can you refresh me on this simple ... A: Let x=the width, and y=the length of the rectangle. The perimeter is 2x+2y, which needs to be 100 ... | |
| Integration | 7/11/2009 |
| Q: I am struggling to integrate x^3 divided by (2-x)^3. Any help would be appreciated. A: Int(x^3/(2-x)^3 dx)...make a substitution: let u=2-x ==> x=2-u, dx=-du Thus, we get: ... | |
| Question about Calculus | 7/9/2009 |
| Q: i really wana solve the questions qhich i m sending you. i actully already solve it but need not ... A: OK... a) Divide each term by x to get: lim(x->oo) (1+2cos(x)/x)/(4+sin(x)/x) .. so the cos(x)/x and ... | |
| Limit | 7/7/2009 |
| Q: How would I find the Limit as x approaches 0 of ((sin(x))/x)^(1/(x^2)) Thank you A: Let y=((sin(x))/x)^(1/(x^2)), now take the "ln" of both sides to get: ... | |
| Tangent Line | 7/6/2009 |
| Q: Let m be a real number and consider the line y=3+m(x-2) and the unit circle (x^2)+(y^2)=1 on the ... A: We can solve this algebraically, although it does get messy. Let's substitute y=3+m(x-2) into x^2 + ... | |
| Calculus Optimization | 6/7/2009 |
| Q: The figure shows two right curcular cones, one upside down inside the other. The two bases are ... A: Since the inner cone is upside down, we establish similar triangles with the large triangle ... | |
| related rates | 6/6/2009 |
| Q: 1.Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile ... A: 1. We differentiate V=(1/3)pi*r^2*h with respect to "t" but first let . r=h/2 (since h=diameter), ... | |
| RELATED RATES WORD PROBLEMS | 6/5/2009 |
| Q: My questions are: 1. A rock is thrown into a still pond and causes a circular ripple. If the radius ... A: 1. Since circumference, C=2*pi*r we differentiate w.r.t. "t" to get . C'=2*pi*r' so you see C' is ... | |
| Calculus | 6/4/2009 |
| Q: an airplane is flying at a constant speed of 360m/hr and climbing at an angle of 45 degrees at the ... A: Since the plane is climbing at a 45 degree angle, we can follow the plane back to the ground so it ... | |
| equations | 6/2/2009 |
| Q: My name is David I am in grade 12 I do not understand Part A (1,2 and 3) on this page: ... A: 1. The vertex of the parabola is at (0,11), so we can write the - equation as y=a(x-0)^2 + 11, as ... | |
| equations | 5/30/2009 |
| Q: I am studying for my diploma exam test can you help me with Part A questions ( 1,2,3) on this page: ... A: 1. The vertex of the parabola is at (0,11), so we can write the - equation as y=a(x-0)^2 + 11, as ... | |
| implicit differentiation | 5/28/2009 |
| Q: How do I do this problem: ln(8y)=4xy Part a) Use implicit differentiation to find the first ... A: a) differentiating with respect to x gives: (1/8y)*8=4y+4x*y', by the product rule = ... | |
| Power Series Integral | 5/27/2009 |
| Q: Use power series to approximate the following integral to six decimal places .5 ∫ln(1+x^4)dx ... A: Since the power series expansion of ln(1+x) is x-1/2 x^2+1/3 x^3-1/4 x^4+1/5 x^5-1/6 x^6+... we can ... | |
| dy/dx | 5/26/2009 |
| Q: How do I do this problem where xy are together? find dy/dx in terms of x and y if 2xy+8x+y=11?? A: Well, in this case we could solve for y in terms of x, then easily find dy/dx...but if the ... | |
| Calculus | 5/25/2009 |
| Q: Use the binomial series to approximate √6 to within .005 A: Sorry for my delay with this...had e-mail problems and did not see this one! The binomial theorem, ... | |
| trig/cal | 5/24/2009 |
| Q: i cannt solve this calculus problem √5cis(1.4) A: By "solve" I gather you mean expand, simplify, or re-write in a+bi form, yes?? If so, then ... | |
| calculus | 5/23/2009 |
| Q: I am having trouble getting the right answers. Can you show me the steps. Given this problem: ... A: V=xy(12-xy)/2x+2y ??? Is that correct? If so, then the two x's divide each other to simplify the ... | |
| math | 1/13/2009 |
| Q: NEED BY TODAY PLEASE!!! In the following exercise, the latitudes of a pair of cities are given. ... A: It may be tough to visualize without showing a diagram, but I will try! Since the two cities are on ... | |
| calculus | 1/12/2009 |
| Q: A bicycle's wheels are 24inches in diameter. If the bike is traveling at a rate of 25 miles per ... A: This is not a calculus question, but... 24 inch diameter = 2 ft diameter. Thus, the circumference ... | |
| thank you | 1/7/2009 |
| Q: evaluate the integral int o to 2a dx int (2ax-x^2)^(1/2) to (4ax-x^2)^(1/2) of (1+y^2/x^2)dy by ... A: I am not clear about the integral. Is there any way you can scan a hand-written version of it so i ... | |
| calculus | 1/6/2009 |
| Q: What is the derivative of X^X^3 for x>0? A: I gather you mean x^(x^3), yes? If so, then we can use "logarithmic differentiation" as follows. ... | |
| newtons law of cooling | 1/4/2009 |
| Q: An aluminum beam was brought from the outside cold into a machine shop where the temperature was ... A: Newton's Law of Cooling/Heating states that the rate of change of temperature of an object is ... | |
| calculus related rates | 12/31/2008 |
| Q: An extension ladder, 17 feet in length against the side of a vertical wall. If the foot of the ... A: Let x=the distance from the base of the ladder to the wall, and let y=the distance from the top of ... | |
| Related Rates | 12/30/2008 |
| Q: The height of a triangle is increasing at a rate of 3 inches per minute while the base of the ... A: Since Area=Base x Height ==> A=b*h, differentiating with respect to "t" gives: A'=b'h+bh', now let ... | |
| describing level curves using polar coordinates. | 9/2/2008 |
| Q: Prof; I need to use polar coordinates to describe the level curves of the function defined by ... A: Polar form often helps one sketch and understand a complicated function. It is not all that obvious ... | |
| finding the derivative | 7/24/2008 |
| Q: i have summer calculas home work to do but i forgot how to do the the derivative part because we ... A: The usual way to take the derivative of this would be via the quotient rule. Thus, a. ... | |
| Calculus applications | 7/19/2008 |
| Q: My questions appears at the very end of this writing, but I thought I’d give you first an idea ... A: It is always satisfying to hear from people who develop an appreciation for or interest in ... | |
| differentiation | 7/9/2008 |
| Q: sir how can i find the derivative of x raise to the power 5/2 by definition method? actually this ... A: Let f(x)=x^(5/2), thus: f'(x)=limit(h->0) [(x+h)^(5/2) - x^(5/2)]/h now multiply by [(x+h)^(5/2) + ... | |
| Related Rates | 7/8/2008 |
| Q: I am having a problem solving a related rates problem. The height of a rectangular box is 10 ... A: Since h is constant, dh/dt=0 and no need to treat h as a variable. So, V=L*W*10 or V=10LW...now ... | |
| derivitive & integral | 1/16/2008 |
| Q: My calc professor said in the first day of class that there's a theory to tie calc 1 & 2 together. ... A: That is pretty vague... I am not sure what he is talking about, as a "theory." I would say that the ... | |
| analysis of functions | 1/8/2008 |
| Q: use a half angle identity to find the exact value of cos 105 degrees A: cos(x/2)=(+ or -)sqrt[(1+cos(x))/2] Thus, cos(105)=cos(210/2)=(+ or -)sqrt[(1+cos(210))/2) = (+ or ... | |
| Cooling Rates | 1/5/2008 |
| Q: One of Julius Sumner Millar's physics questions was: You have made a cup of coffee and the doorbell ... A: Interesting question! Check these link for some answers. The first link "does the math," the ... | |
| problem | 12/31/2007 |
| Q: Let f(x)= êx-a ê+ a and g(x)= 5x +a where a is a positive constant, (a) Use algebra to find, in ... A: OK, so you meant: f(x)=|x-a|+a, yes?? If so, then... a) f(x)=g(x) ==> |x-a|+a=5x+a ==> |x-a|=5x -- ... | |
| AP calculus | 12/29/2007 |
| Q: I'm having trouble with this problem. Find all extrema in the interval [0,2π] if y= x + sin x A: First, y'=1+cos(x)...solving y'=0 gives: cos(x)=-1 Thus, x=pi, for x in [0,2pi], with y''=-sin(x), ... | |
| AP Calculus | 12/28/2007 |
| Q: Let R be the region in the first quadrant under the graph of y = 1/square root of x for 4 <or equal ... A: Looks like you are just giving me a list of your AP Calculus problems...yes? This will be the last ... | |
| AP Calculus | 12/27/2007 |
| Q: A particle moves along the x-axis in such a way that its acceleration at time t for t is greater ... A: a. v(t)=integral[a(t) dt] = 2sin(2t)+C with v(0)=1 ==> C=1...thus, v(t)=2sin(2t)+1 b. ... | |
| Integrals | 12/26/2007 |
| Q: Let R be the region bounded by the parabola y=x-x^2 and the x-axis. Find the equation of the line ... A: The parabola intersects the x-axis at x=0 and x=1. The area is integral(x-x^2,x=0..1)=1/6 Now we ... | |
| double integral | 6/7/2007 |
| Q: How do i calculate the double integral of dxdy/(x^2 + y^2 + a^2)^3/2 where the limits are ... A: Wow, I just found this question of yours from the summer! I had "been on vacation" from AllExperts ... | |
| Calculus | 5/31/2007 |
| Q: 1- The radius r of a circle is increasing at a rate of 2 inches per minute. find the rate of change ... A: 1. A=pi*r^2, so dA/dt = pi*2r*dr/dt - now substitute dr/dt=2 and r=6 or 24 2. V=(4/3)pi*r^3, so ... | |
| Calculus | 5/29/2007 |
| Q: 1- A ladder 25 feet long is leaning against the wall of aa house. The base of the ladder is pulle ... A: 1. Let x=the distance the base of the ladder is from the bldg, and y=the height. Thus, x^2 + y^2 = ... | |
| Calculus | 5/28/2007 |
| Q: 1- A kite is 100 ft.high. There are 260ft. of string out and it is being paid out at the rate of 5 ... A: 1. Using the Pythagorean Theorem: - let h be the length of the string, and x be the - horizontal ... | |
| Calculus | 5/23/2007 |
| Q: I want to know that which book should I refer to so as clear my concept in calculus...I want a book ... A: There are so many available! Here are a few popular ones here in the US: Calculus, by Howard Anton ... | |
| integral calculus | 1/5/2007 |
| Q: how do civil engineers, physicists, electrical engineers, chemical engineers, and economists use ... A: Depends on what they do...not being an engineer, physicist, or economist, I cannot speak about that. ... | |
| calculus | 1/4/2007 |
| Q: If x^2 + 3xy + y^2 = 1 and dy/dt=2 , find dx/dt when y=1. Is the answer dx/dt = 1/2? A: Differentiating with respect to 't' gives: 2x(dx/dt) + 3x(dy/dt) + 3(dx/dt)y +2y(dy/dt)=0 Now ... | |
| trig equation? | 1/2/2007 |
| Q: Please help me!! X is between 0 degrees and 360 degrees (meaning show answer in degrees??) 3sin(x + ... A: Now take the inverse sine (arcsin) to get x+20=-19.47 degrees (approximately This tells us the ... | |
| trig. equation review questions | 1/1/2007 |
| Q: I have two trig questions to ask. 13) solve for x between 0 and 2pi 2sin squared x = 2+ cos2x i ... A: 13) First, convert sin^2 (x) to [1-cos(2x)]/2, to get: 2(1-cos(2x))/2 = 2 + cos(2x), which simplies ... | |
| applications of derviatives | 12/28/2006 |
| Q: A box with a square base is needed to package 100cm^3 of powdered milk. Find the dimensions of the ... A: Let x = the height of the box and y = the length of one edge of the square base Thus, y*x^2=100 ==> ... | |
| conversion | 12/25/2006 |
| Q: How do you convert 20m/s to rad/s? A: Is that 20 meters/second converted to radians/second? If so, then we need more info! rad/sec is an ... | |
| Non-Continuous Functions | 8/9/2006 |
| Q: What are the four times when a function is not continuous? I think one might be when there are ... A: Let's see... 1. vertical asymptotes (caused by a "divsion by zero" 2. when there is an indeterminate ... | |
| Volumes of Revolution | 8/6/2006 |
| Q: I'm trying to find the ways to get these volumes using the washer and shell method. The region is ... A: Washer Vethod: V=Integral(pi*(2^2-[y^(1/3)]^2),y=0..2^3) =Integral(pi*(4-y^(2/3)),y=0..8)=64pi/5 ... | |
| Integration-calculus | 6/8/2006 |
| Q: I have been doing some study for an upcoming test and i have got stuck on one to do with the area ... A: Check these sites for some nice explanations and diagrams: ... | |
| intermediate value theorem | 6/2/2006 |
| Q: how to prove that equation cos x = x has at least one root using intermediate value theorem A: The IVT states: If f is continuous on a closed interval [a,b], and c is any number between f(a) and ... | |
| relationships | 5/24/2006 |
| Q: this question shouldn't take up too much of your time. On a test, my teacher gave this question. ... A: If water enters at a contant rate, then 1. at first, the height rises faster and faster, until -- ... | |
| Word Problem | 5/22/2006 |
| Q: I m in pre-calc, and I have a question about a word problem that is driving me up a wall. I know ... A: Sorry to hear of your health problem...good luck! You left out some info, so I will assume certain ... | |
| Series | 5/20/2006 |
| Q: I am horrible at series. On my math final, it said to evaluate the intergral using Riemann sums 3 S ... A: delta_x=3/n, so... The integral = lim(n->inf) SUM[{(3i/n)^2+2(3i/n)}(3/n), i=1..n] =lim(n->inf) ... | |
| distance and velocity and acceleration | 1/9/2006 |
| Q: I hope I'm finding you in the best of health. A particle starts at time t=0 and moves along the ... A: I just realized I answered 'd' for the original x(t), not the one you gave in 'd'! So, with ... | |
| vectors | 1/8/2006 |
| Q: a wagon is pulled along level ground with a force of 18 N in the handle. if the handle makes an ... A: Think of the 18 N force as the hypotenuse of a triangle. So we have a 30-60-90 right triangle. ... | |
| pre-calculus-hons | 1/4/2006 |
| Q: Is there a simple method to counting principles? thanks, sarj A: Counting problems can be some of the most challenging mathematics problems, even though the methods ... | |
| Simple calculus | 1/3/2006 |
| Q: Working through Morris Kline's Calculus book. I enjoy mathematics but apparenly I don't have an ... A: Let the constant rate of deceleration be -a. So, dv/dt=-a, thus v(t)=-at+vo, where vo=v(0), which in ... | |
| related rates | 1/1/2006 |
| Q: How do you solve this question? Bazooka joe is blowing a sperical bubble gum bubble. Let V be the ... A: Let's differentiate w.r.t. to time 't': dV/dt=(4/3)PI*3*(R+T)^2*(dR/dt + dT/dt) - ... | |
| calculus | 12/29/2005 |
| Q: the illumination at a point is directly proportional to the intensity of the light source and ... A: Sorry for my delay... Let x=the distance from source L1, thus s-x=the distance from source L2. The ... | |
| calculus | 12/23/2005 |
| Q: What does it mean to take a deravitive? I would also like to know if you have read The Road to ... A: To "take a derivative" of a function, generally means to express the instantaneous rate of change, ... | |
| hi | 9/17/2005 |
| Q: Im a college student from so cali. i have a test on wednesday. im in business calc and i have ... A: OK, we need to take the limit as h-->0 of [f(x+h)-f(x)]/h first let's do [f(x+h)-f(x)]/h, to get: ... | |
| Hello | 9/16/2005 |
| Q: My question isn't so much about how to do certain things in math, but rather how useful it is in ... A: True, there are many successful (as measured by income) people who have weak math skills! However, ... | |
| calculus | 9/14/2005 |
| Q: i want to know how to take the integral of 5x divided by the square root of (5x minus 3x to the ... A: So, you want to solve: Integral(5x/sqrt(5x-3x^2) dx) yes? If so, then first complete the square on ... | |
| Calculus | 9/9/2005 |
| Q: Determine whether the points lie on straight line. a) (5, 1, 3) (7, 9, -1) (1, -15, 11) Determine ... A: a) a vector from (5, 1, 3) to (7, 9, -1) -- is [7-5,9-1,-1-3] = [2,8,-4]=V1 -- a vector from (7, 9, ... | |
| Multivariable Calculus | 9/8/2005 |
| Q: Find two unit vectors orthogonal to both <1, -1, 1> and <0, 4, 4>. A: The cross-product of two vectors yields another vector that is orthogonal to the two of them. Thus, ... | |
| Functions, graphing | 9/5/2005 |
| Q: I'm gonna go out on a limb here and ask 3 questions/problems. Even if you only answer 1 that would ... A: 1. (a) (f+g)(x) is short for f(x)+g(x), so... ------ (f+g)(x)=x/(x+1) + x^3 ---(b),(c), and (d) are ... | |
| Applications of Integrals | 9/3/2005 |
| Q: I would appreciate it if you could check my answers. I'm sorry it is so long. 1.) Let R denote the ... A: You have quite a few questions! Let me just help you with the first two for now...if you still need ... | |
| Limits | 9/2/2005 |
| Q: I am studying for a test and one of the problem has an x with a vertical arrow and the infinity sign ... A: Wow, a test already! Didn't classes just start?! :-0 Anyhow... Is the vertical arrow pointing ... | |
| calculus (limits) | 8/30/2005 |
| Q: i am a highschool senior in calculus b/c and i have a real general question about limits. what is a ... A: The major idea of a limit is what value does a function "appear" to be approaching, irrespective of ... | |
| Calculus | 8/29/2005 |
| Q: I have used the rule: Integral(dx / x^2 - a^2) = 1/2a ln (absolute vale of)(x-a)/(x-b) + c to get ... A: Should the limits of integration go from x=0 TO x=pi/2 (rather than the reverse)? If so, then I get ... | |
| Calculus | 8/28/2005 |
| Q: 1. You start 60 miles east of Pitsburgh and drive at a constant speed of 50 miles per hour (assume ... A: Also, please post your questions in the appropriate group...this is an algebra question, not ... | |
| Calculus | 8/27/2005 |
| Q: How is the integral of sin x / 1+sin^2 x found? A: I gathe you mean: Integral(sin(x)/(1+sin^2(x)) dx)...yes? If so, then let u=cos(x), so that ... | |
| math | 8/26/2005 |
| Q: if it is not possibly to solve tell me why?if it is then solve it the sum of five consecutive ... A: In the future, please direct your questions to the appropriate group...these are NOT calculus ... | |
| Calculus 1 | 7/10/2005 |
| Q: Can you give me a couple of problems to practice with in the area of limits, piecewise functions, ... A: Try these: http://archives.math.utk.edu/visual.calculus/1/limits.15/ ... | |
| Questions | 7/9/2005 |
| Q: Q 1 Find surface area of paraboloid S by revolving graph of y=x2 between x=0 and ... A: 1. You did not finsh with the limts...between x=0 and ??? 2. There are various densities of ... | |
| Surface Area | 6/5/2005 |
| Q: How would one go about finding the surface area of the sphere: x^2 + y^2 + z^2 = 4 that lies above ... A: There are a few ways...depending on how much math you know. Are you in a calculus class? Single or ... | |
| Calculus Integrals | 5/30/2005 |
| Q: Integral of (2sin(3x)-4cos95x))dx i know you have to probably use U sustitutionon all of them but i ... A: 1. Int(2sin(3x)-4cos(5x)) dx = 2cos(3x)/(-3) - 4sin(5x)/5 + C = -(2/3)cos(3x)-(4/5)sin(5x)+C ... | |
| question about AP | 5/25/2005 |
| Q: i have a question about taking AP Calculus. what do u need to do in order to prepare for AP Calc b/c ... A: Of course, as with nearly any math course, you need certain skills in advance! For calculus, you ... | |
| Prime numbers | 5/24/2005 |
| Q: How many prime numbers between one and one million become perfect squares when 1 is added to them ... A: BTW: there are 78498 primes between 1 and 1000000... Hello Maxine, Only One! Namely, 3 ... | |
| Throwing a Ball-- Math Problem | 2/6/2005 |
| Q: I'm taking a History of Mathematics class and I'm working on a few math problems that I'm having ... A: A) D(T)=(1/2)gT^2+VoT+Do -- where g is about -32, Vo=-40, Do=600 -- so, D(T)=-16T^2-40T+600 B) Just ... | |
| Metric conversions | 2/6/2005 |
| Q: I'm in a Pharmacology class and it's been awhile since I've had any math dealing so in depth with ... A: Here are some useful websites for you: http://www.easysurf.cc/cnver8.htm ... | |
| integral problems with velocity | 2/4/2005 |
| Q: let say at t=0, a ball was dropped from a height of 16ft. it hit the ground and rebounded to a ... A: for the first part (from 16 ft drop to the floor): v1(t)=-32t, 0<=t<=t1, t1=time until ball hits ... | |
| Optimizing | 1/23/2005 |
| Q: I have three Calculus Questions that I have worked on for three hours and I can't figure them out. ... A: 1. Let x=length & y=depth, with 4=width, and volume, V=36 -- so, 4xy=36 ==> y=9/x -- the area of the ... | |
| Differential and Integral calculus | 1/17/2005 |
| Q: Basic questions: What is the purpose of trigonometic functions in Calculus? What is the purpose of ... A: Trig functions are useful to describe phenomena that is periodic...such as problems involving ... | |
| Characteristic Polynomials | 1/15/2005 |
| Q: What is a characteristic polynomial? A: Check these references: http://mathworld.wolfram.com/CharacteristicPolynomial.html ... | |
| Functions | 1/14/2005 |
| Q: got one more quick one no one seems to know using implicipt differentiation find the equation of the ... A: .. Differentiate with respect to x, so we get: 3x^2+2xy'+2y+3y^2y'=0 (using the product rule for ... | |
| Identities | 1/11/2005 |
| Q: i dont know where to start with this problem; Prove that the equation is an identity sinX/(1-cosX) ... A: OK, combine the left side by getting a common denominator, which is sin(x)[1-cos(x)]: ==>[sin(x)^2 + ... | |
| Calculus | 1/10/2005 |
| Q: I'm having trouble solving this problem, and was wondering if you could help me with parts b and c. ... A: (a) (-sqrt(3),-sqrt(3)) & (sqrt(3),sqrt(3)) (b) V is just the difference in y-values. --- since the ... | |
| Max Area | 1/9/2005 |
| Q: A little help What is the Max Area of a redtangle inscribe in the ellipes x^2+4y^2=4 with the sides ... A: Yes, that is a good start! Actually, y=(+/-)(1-x^2/4)^(1/2), i.e. plus or minus... So the dimensions ... | |
| Optimization Problems | 1/8/2005 |
| Q: The lifeguard at a public beach has 400 m of rope available to lay out a rectanguluar restricted ... A: I need to know if this is for a precalculus class or calculus? There are two ways to do ... | |
| Use Lagrange or other method?? | 1/4/2005 |
| Q: I would like to know "a grosso modo" the type of problems in wich i MUST use Lagrange multipliers ... A: Whenever you have a max/min problem (in more 2 or more variables) WITH CONSTRAINTS, then you use ... | |
| Calculus | 12/26/2004 |
| Q: Let f be the function given by f(x)= (2x)/((x^2)+x+1)^.5 Find the range of f. Use f'(x) to justify ... A: Notice that limit (as x-> +infinity) of f(x)=2 and limit (as x-> -infinity) of f(x)=-2 Now for the ... | |
| Integration | 1/28/2004 |
| Q: I am having problems solving the following definite integraL The integral from 0 to 2^.25 of: ... A: Yes, good substitution! Let u=x^4, so du=4x^3 dx Thus, the integral becomes: ... | |
| calculus | 1/25/2004 |
| Q: I need to solve the equation z to the 5 = i Please help! A: z^5=i=1*e^(i*T), where T=pi/2...using DeMoivre's Thrm... z=1^(1/5)[cos(T/5)+i*sin(T/5)] or ... | |
| Related Rates | 1/7/2004 |
| Q: The question is: A radar station is 2000 ft from the launch site of a rocket. if the rocket is ... A: Let x=the distance from the rocket to the radar station, which will be the hypotenuse of a right ... | |
| High School level Calculus | 1/3/2004 |
| Q: How would I go about solving this problem: The problem gives me the solution of y= The integral ... A: Well, just take the first and second derivative of the given solution, substitute them in to the DE ... | |
Calculus
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Abe Mantell
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Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
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