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Homework Help: Derivative homework

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Can someone check my homework?
    http://img10.imageshack.us/img10/9686/48742895.jpg [Broken]
    http://img229.imageshack.us/img229/6981/52780988.jpg [Broken]
    http://img297.imageshack.us/img297/6955/85086758.jpg [Broken]
    http://img11.imageshack.us/img11/1221/86324492.jpg [Broken]
    thx!

    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 8, 2010 #2

    Mark44

    Staff: Mentor

    Re: Derivative

    In problem 2 you have a mistake.
    You have
    C = 2sqrt(A*pi) = 2(A*pi)^(1/2) = (A*pi)^(-1/2) *pi

    The 2nd and 3rd expressions above are not equal. You have apparently taken the derivative, but you show it as being equal to C. The derivative of C is not equal to C.
     
  4. Feb 8, 2010 #3
    Re: Derivative

    Oh, I forgot to put C'!
    Is that the only mistake i got?
     
  5. Feb 8, 2010 #4

    Mark44

    Staff: Mentor

    Re: Derivative

    You got the right answer, but make sure you understand the difference between C'(A) and C'(81)

    C'(A) = sqrt(pi/A)
    C'(81) = sqrt(pi/81) [itex]\approx[/itex] .1969

    Another way to write what you're doing is this:

    [tex]\frac{\Delta C}{\Delta A} \approx \frac{dC}{dA}[/tex]
    [tex]\Rightarrow \Delta C \approx \frac{dC}{dA} \Delta A[/tex]
    [tex]\Rightarrow \Delta C \approx \frac{dC}{dA}|_{A = 81} \Delta A[/tex]
    [tex]\approx .1969 * 1 = .1969[/tex]

    Everything looks fine for the other problem.
     
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