Karl's Calculus Forum

Here is your chance to discuss calculus topics with your fellow students, teachers, and other visitors to Karl's Calculus Tutor. Feel free to post problems that are challenging you as well as solutions to problems that others have posted. You may also post comments or criticisms of the materials that you have found on Karl's Calculus Tutor. I will be reading the postings here frequently. I will also, from time to time, post problems here to stimulate discussion.

Please remember that these are family webpages, so keep your comments tasteful and in good spirits.

**Archives of previous months' forum:**
See July-December 2006 entries See January-June 2006 entries See Summer/Fall 2005 entries See May/June 2005 entries See March/April 2005 entries See January/February 2005 entries See November/December 2004 entries See Sepember/October 2004 entries See Summer 2004 entries See Spring 2004 entries See February/March 2004 entries	See December 2003/January 2004 entries See October/November 2003 entries See September 2003 entries See July/August 2003 entries See June 2003 entries See May 2003 entries See Apr 2003 entries See Mar 2003 entries See Jan-Feb 2003 entries See Dec 2002 entries See Nov 2002 entries	See Oct 2002 entries See Sep 2002 entries See Summer 2002 entries See May 2002 entries See Apr 2002 entries See Mar 2002 entries See Feb 2002 entries See Jan 2002 entries See Dec 2001 entries See Nov 2001 entries See Oct 2001 entries

The form-entry page contains instructions for entering math notation. Please read them carefully, otherwise your posting might turn out illegible.
Post Your Message to the Forum

Current Forum Discussion Begins

Hey, I had this calculus problem and was wondering how to the derivative of the following function (it's using implicit differentiation).

  x² + y²=25

I got
         x
        ---
         y


as the first derivative but am a bit confused on the second, I'm aware that I have to use the quotient rule, but I am getting a really weird answer...  help is appreciated please

Thanks

Safiya

Safiya







Amman, Jordan - Saturday, October 31, 2009 at 13:57:32 (EDT)

I honestly dont understand why im not getting this... even with using trig identities i cant find how they get the answer... help if you could please! Calc II.

int. cos³(x)sin(x)d(x)


the answer should come out to be:
-1/4 cos ⁴(x) + C

if you could show me the process that would be great... thanks!

Emily







phoenix, az USA - Thursday, September 24, 2009 at 19:48:49 (EDT)

Folks, for simple clear and concise video explanations of Single Variable Calculus, go to ViewMath.com a brand new site. No frills no gadgets just a smart guy with a blackboard.
Leo Valk

katy, tx USA - Wednesday, September 16, 2009 at 07:49:35 (EDT)

i am a sener an i need help with cal frist year thank you forest elkins
forest elkins

itasca , tx USA - Monday, August 31, 2009 at 22:49:42 (EDT)

i wanna know much about karlculus. because i am damned interested in the website
MUHAMMAD MUSTAPHA

zaria, kaduna nigeria - Monday, August 10, 2009 at 13:06:34 (EDT)

Please help me with this, I cannot figure it out. I am so confused! Find the equation for the line tangent y= 5-4xsquared at (-3,-31)
Mary

utica, ny USA - Tuesday, July 21, 2009 at 16:41:18 (EDT)

I am having a problem finding the second derivative for the follwing problem. I know I am just doing something dumb and not comming up with the right answer. Please help! f(x)= x^{(4/7)

Thanks in advance for the help.

David

Merlin, Wi USA - Monday, June 29, 2009 at 15:31:19 (EDT)}

I have no calculus background and I need to know how to find the area under an arc. I believe calculus is what would used to determine the answer. The area I am concerned with is mostly rectangular: Left side= 26', bottom= 150', right side= 26'. The top has an arc with the middle being @ 75'. Is there a formula I could use to plug in these values and find the answer and use it continually as a template.
Charles

Asheboro, NC USA - Friday, April 24, 2009 at 10:55:00 (EDT)

I am struggling with proglem and hope you can help. "A particle is moving along the x-axis with a velocity of v(t)= 5te^(-t) - 1. At time t=0, the particle at x=1. How far does the particle travel from t=0 to time t=4." My gut tells me I need to do an indefinite integration on v(t) amd use the the point (0,1) to determine C. Then I need to do an indefinite integration on that position function from 0 to 4. The problem is the 5te^(-t) has me stumpted. It the product that does not work. I have tried to move the t behind the e^(-t) and use it as part of the derivative but it does not work. I have tried to use "u" for -t but that still does not help. Any suggestions? I am in calc I. Thanks
Sue

Pierson, Fl USA - Sunday, March 15, 2009 at 19:59:27 (EDT)

a cup of coffee is heated to a temperature of 100 degrees. the cup is then left on the counter of a room with a constant temperature of 68 degrees, and after a minute, the temperature of the coffee has dropped to 95 degrees, and after another minute it has dropped to 92 degrees. how much time before the temperature of the coffee has dropped to 70 degrees? using newton's law of cooling
bailey

NY USA - Sunday, March 08, 2009 at 15:34:58 (EDT)

Ok, so I'm doing some calculus (pre-calc II) WAAAAYYYY after high school. Let's just say I've been in the Navy for 14 years to give a rough estimate. I would LOVE to understand how


if π<θ<3π2 then π2<θ<3π4, θ is in quadrant 2

So, I previewed the notation, and I can't get it to come out right. The verbiage for this question is thus: if pi is less than theta is less than 3 pi over 2, then pi over 2 is less than theta over 2 is less than 2 pi over 4, so theta is in quadrant 2. I sent myself dangerously close to the brink of insanity trying to visualize this on graph. Thanks for any help! Chris
Chris Stratton

Honolulu, HI USA - Thursday, November 06, 2008 at 00:23:39 (EST)

What is the derivative of

 y²(y²-a²)=x²(x²-b²)

Joe







BHC, AZ USA - Wednesday, November 05, 2008 at 12:30:21 (EST)

I am having problems with an advanced calculus question. I need to find two functions f,g that do not have limits at x naught but f+g has a limit at x naught. Similarly, fg with a limit at x naught and f/g with a limit at x naught. How do I go about coming up with the functions to use? Would a number other than zero be best for x naught?
Melissa

Prairie du Chien, WI USA - Sunday, November 02, 2008 at 11:51:14 (EST)

Umm, i'm a bit confused here. I'm in a Pre-Calc class at my school, can I still use this site? I went to the Regents Prep. Org page and it linked me here.
Kathleen W

New York, NY USA - Saturday, October 04, 2008 at 20:21:14 (EDT)

Reply to Caitlin: When you plot, for example, 1 = (x³/k) -(y/k), you are plotting the contour for f = 1. To plot that, you need to rearrange the equation slightly to

y = x³ - k

I arrived at that by multiplying by k, subtracting k from both sides, then adding y to both sides. For the contour at f = 2, you would plot

y = x³ - 2k

and so on for each contour you wish to plot. Note that the contour values need not be positive integers. In general, if you want to plot the contour at f = r, plot

y = x³ - rk

where r is any real number.

Also please note that one of the two equations you typed into your question has a mistake. I think you meant that f(x,y)=(x³/k)-(y) should have been f(x,y)=(x³/k)-(y/k).
Karl
USA - Monday, September 15, 2008 at 18:33:05 (EDT)

I am having difficulty with contour graphs. For example, I have to graph f(x,y)=(x³/k)-(y). I can get the equation to look like: 1 = (x³/k) -(y/k) but I do not know how to graph this.
Caitlin

USA - Monday, September 15, 2008 at 16:27:33 (EDT)

Reply to Moira Weigel: I think this is something of a trick question. Observe that the constraint does not in any way involve k. So if f is maximized by some x₁, ..., x_n that meets the constraint, then k f is also maximized by that same solution. So the partials with respect to k of each of the x_j components would necessarily be zero. Why? Because the solution is unaffected by your choice of k, as long as k ≠ 0.

Also, observe that if you apply Lagrange multipliers to the original maximization problem, it too will result in a solution that is independent of k.
Karl <Click to Send Email to Karl>
USA - Friday, August 08, 2008 at 19:03:09 (EDT)

Could someone help me with this constrained optimization problem? Let x₁(k,c) ... x_n(k,c) be the solutions to the problem:

  Max      k*f(x₁, ... , x_n) subject to g(x₁, ... , x_n) = c
 x₁, ... , x_n

as functions of the parameters k and c. What are the formulas for the partial derivatives:

 ∂x₁(k,c)/ ∂k   ∂x₂(k,c)/ ∂k   . . .  ∂x_n(k,c)/ ∂k

(assume that k is initially strictly positive and remains positive)
moira weigel

cambridge, ma USA - Tuesday, August 05, 2008 at 18:22:40 (EDT)

I'm trying to set up minimization and constraint equations. On the surface, the problem looks easy enough: minimize the amount of material to make a 163 ml juice can. Okay...so I figured the area formula to be 2*Pi*r^2+2(163/r), which differentiates into 2*Pi*r+326/r^2. We'll solve it for 0, which results in 2.96 cm for the radius. Moving right along...this can is first cut from a sheet divided into squares with circles inscribed in them, which is easier but produces more waste material. Then this can is cut (more efficiently) from a sheet divided into hexagons with circles inscribed in them. How do I involve this information with the problem at the beginning of the post to minimize the amount of material in both cases? I would have assumed I simply needed to come up with a constraint equation, then provide area sums for both sheets, but there are blank spots for the new radius and height which implies that I'm missing something.
Chelle

USA - Thursday, May 15, 2008 at 10:21:21 (EDT)

i have a math prob. about airplane position, velocity.. 2 airplanes are in a straightline landing pattern and must keep at least a 3 mi separation. airplane a is 10 mi from touchdown, and is gradually decreasing its speed from 150 mph to 100 mph. Airplane B is 17 mi from landing and is decreasing its speed from 250 mph down to 115 mph. A) assuming the deceleration of each plane is constant, find the position functions s1 and s2 let t=0 represent the times when the aiplanes are 10 and 17 mi from the airport. B) find a formula for the magnitude of the distance d between the 2 planes. is it less than 3 at some time? if so find that time.
Rachel Vander Ploeg

lawton, mi USA - Saturday, April 12, 2008 at 16:13:21 (EDT)

ANy chance of an answer? Integration from +Infinity to -Infinity of the following e to the power of -x/SqRoot(4*pi*D*t) * sin (n*Pi*x/2) dx Set by my son so I would like to surprise Thanks
Richard

USA - Friday, March 14, 2008 at 11:28:37 (EDT)

The following Problem: A mass accelerated in a straight line from Zero V0 to Vend. What is the delta ΔkW consumption(indication on the kW meter)for every delta displacement(gain in distance ΔS of the mass???? Let Vm =intermetiate attained (staircaise)Velocity at attaind displacement, Let m=Mass, let Δv = delta velocity(gain in velocity per gain to the distance), let Δs = delta Displacemet(delta distance or incemental distance), let Δe = delta ΔkW power flow,


                Δv^{2
        (Vm^{2 + ---------- ) * m * Vm
                   2
Δe(kw) =------------------------------------
                Δs}}

IS THIS FORMULAR CORRECT?????
Gottfried Gutsche

Mississauga, Ont Canada - Wednesday, March 12, 2008 at 12:53:38 (EDT)

1. The problem statement, all variables and given/known data
1) If f(x)= sin^4x, then f '(pi/3)
2) Given f(x) = x/tanx, find f '(3pi/4)
3) If f(x) = sinxcosx, then f '(pi/6)
4) Differentiate: f(x) = x^2 + 2tanx
Question that I have answered but not sure if it's really the right answer:
5) Find the equation of the tangent line to the graph of f(x) = (x-1) / (x+1) when x = 1
2. Relevant equations
Product Rule?
* y= f x g
F'g + g'f

Chain Rule?
* y=f / g
* ((f'g) - (g'f)) / ((g^2))

Slope?
* y=mx+b

3. The attempt at a solution
1) f(x) = sin^4x then f '(pi/3)
Derivative of sinx = cosx therefore...
I'll assume that sin^4x has the derivative of cos^4x
Now, plug in the number...
cos^4(pi/3) = 0.065
Is that right?
2)
Given f(x) = x/tanx, find f '(3pi/4) Chain Rule:
((f'g) - (g'f)) / (g^2)
Therefore... ((1 * tanX) - (??? * X)) / ((tanx^2))
Let * be multiplication sign and the ??? to be the "I don't know".
So, I got stuck of what the derivative of "tanx". However, what I do know is that:
tanx = sinx / cosx
tanx' = cox / -sinx <-------Is that right?
If yes, then how am I suppose to make my equation by using "cox / -sinx "? By plugging that in... I get this:
(((1 * tanX) - ((cox / -sinx) * X))) / ((tanx^2))
Then I'm really stuck on that one... I mean, if I do plug in the "pi/3" to the "x" variables then it will just be a mess. Unless that's the only way to get the answer? Or should have I used the product rule instead?

3)
If f(x) = sinxcosx, then f '(pi/6)
Product rule:
y= f x g
F'g + g'f
Therefore...
= (cosx*cosx) + (-sinx*sinx)
= (cos^2x) + (-sin^2x)
= (cos^2(pi/6)) + (-sin^2(pi/6))
= 0.633
-Let * be a multiplication sign
-Is that right?

4)
Differentiate: f(x) = x^2 + 2tanx
So, I'll just get the derivative of the equation...
2x + 2(???)
-Let ??? be "I don't know".
So, I'm stuck. I have no idea what's the derivative of tanx have. I already encountered this problem in question #3 and I assumed that it would be:
tanx = sinx / cosx
tanx' = cox / -sinx
Is that right? If yes, then I would get this equation:
2x + 2(cosx/-sinx)
Is that right? If yes, can I simplify it much more?

5)
Find the equation of the tangent line to the graph of f(x) = (x-1) / (x+1) when x = 1
y=mx+b
Chain Rule:
= 1(x+1) - 1(x-1) / (x+1)^2
= x+1 -x +1 / (x+1)^2
= 2 / (x+1)^2
= Plug in "x"
= 2 / (1+1)^2
= 2 / 4
= 1/2
slope (m) = 1/2
Now that I have the slope, I'll just get the x & y values from plugging in "1" to the equation.
y = (1-1) / (1+1)
y = 0/2
y = 0
So: x = 1 and y = 0
Then reflect on the slope equation:
y = mx+b
Plug in the numbers from what I have gotten before:
0 = 1/2(1)+b
0 - 1/2 = b
-1/2 = b

So...
y = 1/2(x) + (-1/2)
I'll multiply the whole equation by "2" to make it more neater.
2y = 2(1/2x) + 2(-1/2)
2y = x -1

Is that right?

------------------------------------------
I know my solutions were kind of long. But I hope that you could help me. I really want to make this happen. Or at least answer the questions correctly or in a much simplified way. =)

PLEASE.
paola

Canada - Wednesday, March 12, 2008 at 00:48:16 (EDT)

Okay. I've been working on this problem for a solid two, front and back, notebook pages. Can someone please tell me if I'm on the right track with this? Differentiate: y=x^x 1. I took the natural log of both sides. ~ lny= xlnx 2. I used the formula, [lnu]= u'/u, for the xlnx ~ lny = x(1/x) 3. I " e'd" both sides to get rid of the natural log of y. ~ e^lny ******* 4. This is where I'm kind of stuck. I dont know which of the following should be the outcome of my "e-ing"... a. y= xe^(1/x) or b. y= e^(x(1/x) This could be an easy answer, but I'm a little confused. Could someone please help me?
Ariel

Cambridge, MN USA - Monday, March 10, 2008 at 21:41:29 (EDT)

Hi, A question. have you heard of the smoothstep function. So if you have heard of this function then this question is for you. Their exists a 3 degree polynomial function whose derivative is a solution to a smoothstep function. i.e.


f(x) = ax³ + bx² + cx + d

when drawn the derivative of this function gives a curve as shown in image Fig 1. What is needed is a shown in Fig 2. Is it possible. How. ? PS, Since it is not possible to load an image here. Imagine Fig 1 as a less curvy 'S' and Fig 2 as a normal 'S' BRgds, kNish
knish

mumbai, MAH India - Friday, January 04, 2008 at 04:25:17 (EST)

Water is flowingat the rate of 6m^3/min from the tank shaped like a hemispherical bowl of radius 13m. Answer the following questions given that the volume of water in a hemispherical bowl of radius R is: V = (pi/3)y^2(3R-y) when the water is y meters deep.

a. at what rate is the water level changing when the water is 8in deep?

b. what is the radius r of the water's surface when the water is y in. deep?

c. at what rate us the radius r changing when the water is 8m deep?
Adam

kingston, pa USA - Sunday, November 11, 2007 at 00:38:43 (EST)

General info. I discovered a clear explanation of the Related Rate Problemin Calculus, J.Stewart., 4th Ed.
Robert

Dingmans ferry, PA18328General info: USA - Wednesday, November 07, 2007 at 15:19:40 (EST)

y^{x^-1} = y^1/2 * ln(y^{x^-1}) Is there a way to rearrange this equation is terms of x? i.e. x=?????? so I can solve it (without calculus) by just plugging in a y? Assume y >= 1, limit to natural numbers if necessary. I only need positive, real solutions for x. How do I solve for x when x is a root of a natural log? I think I could do it if there was only one x, or if there was no log. But with two x's and one in a log, I don't know how to rearrange this so x is by itself on one side of the equation.
David

Surrey, BC Canada - Thursday, October 25, 2007 at 19:31:00 (EDT)

I need some help on the following to determine whether or not they are continuous and explain why or why not: Is f(x) = 5x-10 continuous at x=2? Help would be greatly appreciated. Malga
Malga

USA - Sunday, October 21, 2007 at 15:55:49 (EDT)

I'm having problems trying to graph these conditions. I don't know where to begin. Please HELP!! 1. Sketch the graph of a function f(x) that satisfies the following conditions: a)f(-9)=f(1)=f(6)=0, b)f'(-4)=f'(3)=0, c)f"(-8)=f"(-1)=0, d)f'(x) positive only on (-4,3), e)f"(x) positive on (-8,-1) and (8,infinity). On graph, label all the points of inflection, local maximum, and local minimums.
NETTE

Denver, CO USA - Tuesday, October 09, 2007 at 03:43:30 (EDT)

given P = Y^tY - 2Y^tAC +C^tA^tAC Where Y is a column vector = a matrix with rows n and column =1. A is a matrix rows = n cols = 2 the first col are x, that is x1, x2,...,xn; the second col has 1 in each entry. C is a colum vector = a matrix with 2 rows and one column call the entries c1 & c2. ^t symbolizes transpose The equation for P reads in English: (Y transpose by Y) minus (twice times Y transpose by A by C) plus (c transpose by A transpose by A by C) I want to find the partial derivative of P with respect to c using the rules of linear algebra. I know the solution is -2A^tY +2A^tAC, in English minus (times A transpose by Y) plus (twice times A transpose by A by C) I am unable to locate a reference giving details on how to evaluate a derivative using the rules of linear Algebra with simple examples for me t work with. I have expanded written out P using n=2 and then found the partial derivatives using the normal rules for functions of two variables. It was most tedious and I would like to learn the linear algebra rules based on simple examples. Many thanks, Peter
Peter

Ireland - Monday, October 08, 2007 at 04:41:44 (EDT)

I am taking a distance learning Calculus course. I have been out of school for 15 years and was never very good at the maths in the first place. I am pulling my hair out trying to figure out a problem that should be simple. How do I approach it? Here it is: A car rental agency has rates of $75/day (with partial days charged at the full day rate) and $330/week. You are charged the daily and/or weekly rate, whichever is cheapest for you. For example, if you rented a car that was $100 daily or %50 weekly, the charge for 4 days use would be $400; the charge for 6 days use would be $550; the charge for 8 days would be $650 ($550 + $100) Let A(t) represent the average cost to rent the car for t days, where 0 < t < or = 15 I am confused and at a dead end.
Jordan Hyde

Springville, UT USA - Tuesday, September 25, 2007 at 18:05:58 (EDT)

[Question] Hi, my teacher gave us this problem, and he couldn't figure out why method was incorrect and why I got the answer I did. Given we know the gradient slope = <-56,1.886> at the point (2,0) on a surface f(x,y), in what direction, expressed as a unit vector, is f increasing most rapidly? [Difficulty] I solved the problem like this: Max slope = magnitude of gradient slope (gradient slope) dot (unit vector) = 56.03 -56.03Ux + 1.866Uy = 56.03 sqt(Ux^2 + Uy^2) = 1 Solving the system Ux= -.9977 Uy=.0672 The only problem is, by definition, I should be able to get the unit vector by taking the gradient slope vector and dividing by the magnitude of the gradient vector. or, <-56/56.03, 1.886/56.03> = = <-.9994,.0336> The weird thing is, the correct Uy value is almost exactly half of mine...what's going on??? [Thoughts] I tried a similiar technique for finding where the ∇f = 0 <-56, 1.866> dot (unit vector) = 0 -56.03Ux + 1.886Uy = 0 sqt(Ux^2 + Uy^2) = 1 Solving the system this time I got the correct answer, why here and not there?
John Smit

USA - Wednesday, September 19, 2007 at 00:05:15 (EDT)

l would like to join your program, to send and receive calculus problems. lam very good in math and l hope to enjoy your program with other students
stephen nyamapfumba

houston, texas USA - Saturday, September 15, 2007 at 19:52:41 (EDT)

Hi,

I have not done calculus in a while. Find the range for:

g(z) = 1 / square of 4-z^2

I can easily find the range for the other equations but I got stuck on this one since it's 1 / over a square, etc.

Thank you.
Martyn Reno

Montreal, QX Canada - Thursday, September 13, 2007 at 22:17:51 (EDT)

hey, can anyone help with solving equations by extracting square roots
varawdn
USA - Saturday, September 08, 2007 at 19:32:08 (EDT)

Can ε = 1/δ ? I mean such function should not have a limit, because as delta gets smaller epsilon gets bigger so function is not converging. Am I right?Thank you in advance very much.
felix

USA - Friday, July 20, 2007 at 11:38:04 (EDT)

A piece of wire 5 inches long is to be cut into two pieces. One piece is x inches long and is to be bent into the shape of a square. The other piece is to be bent into the shape of a circle. Find an expression for the total area made up by the square and the circle as a function of x. I need this to be as detailed as possible. I got the final formula...I don't know if it's right, or if I have to put it into the y=^#$*&^$^ form. So, if you could answer both of those questions, that would be EXTREMELY helpful.
Katie & Annamarie

USA - Thursday, July 12, 2007 at 15:03:35 (EDT)

Reply to Chase. If it is a simple graph here is what you need to think about: The graph of cos & sin repeat after 2pi or 360 degrees, the period The graph of cos & sin has a y distance from max to min of 2 units The graph of cos & sin is centred about y=0 look at your graph, think of it as a sin graph, what is its period? if it is 120 degrees then it is the graph of 3x if it is 720 degrees then it is the graph of 0.5x, call this number a. Does it pass through 0 and it it increasing to the right of 0? if not it is the graph of a sin but shifted to the right or left so it needs to be written as sin(x + - some number), call this number b, if a from above is not 1 you need to write this as sin(ax +- ab). What is the y distance from the max to the min? if it is not 2 then you need to multiply sin(ax +- ab) by some number C that is greater than or less than 1: Csin(ax +- ab). Is the graph centered about y=0? if not you need to add or subtract some number D to get Csin(ax +- ab) +- D. Hope this helps Peter
Peter

Ireland - Monday, June 11, 2007 at 09:06:21 (EDT)

How do you write an sine and cosine equation from a graph?
Chase

fort smith, ar USA - Tuesday, May 29, 2007 at 23:17:14 (EDT)

I need help with finding simultaneous tangent lines for two equations f(x)= ln x and g(x)= e^x I have looked at the problem that was sampled but I am having troubles doing the substitution of f(x) and g(x) when trying to solve for one of the variables.
Josh

md USA - Tuesday, May 15, 2007 at 21:38:24 (EDT)

Reply to Mark: Just because an expression seems simple, it doesn't mean that it's easy to integrate. The antiderivative of your function cannot be expressed in any finite combination of elementary functions. Indeed you need to use Jacobian elliptic integral functions in order to integrate this. That is a topic that is usually not covered in first and second year courses.
Karl <Click to Send Email to Karl>
USA - Friday, March 30, 2007 at 15:25:35 (EDT)

This is a great site, and has kept me entertained for countless hours rediscovering my "A" level maths (I guess that equates to High School for those of you [no doubt the majority] on the other side of the pond!). I've set myself increasingly complex problems until I've finally stumped myself! I'm trying to integrate the following pretty simple expression:

f(x)=√(1+kcos(x))

I've tried the route of substituting x=arccos(w), x=arccos(w/k) and various mungeing ideas. I've tried expressing the resultant as logs, but no matter what twists and turns I try, I can't get it to fall out. If anyone has any clever ideas I would be very grateful to hear from you.

Many thanks,
Mark
Mark

Croyde, Devon UK - Thursday, March 29, 2007 at 10:23:13 (EDT)

I need help with calculus (integrate), out of school too long.
Charles Carter

Vine Grove, KY USA - Monday, March 26, 2007 at 14:02:26 (EDT)

Reply to Jesse: There is an almost identical problem to this in the online webpages. Please click here to see the worked solution. Then see if you can apply the same method to your problem.
Karl <Click to Send Email to Karl>
USA - Friday, January 05, 2007 at 12:53:05 (EST)

A spotlight on the gound shines on a wall 12 m away. If a man 2 m tall walks from the spotlight towards the building at a speed of 1.6 m/s,how fast is the shadow on the biulding decreasing when he is 4 m from the building?
Jesse

Los Angeles, California USA - Thursday, January 04, 2007 at 19:11:23 (EST)

Scripts and Message Board created by Matt Wright and can be found at Matt's Script Archive

You can email me by clicking this button: