Derivative homework

  • Thread starter Nope
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  • #1
100
0

Homework Statement


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!

Homework Equations





The Attempt at a Solution

 
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Answers and Replies

  • #2
35,135
6,884


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.
 
  • #3
100
0


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.

Oh, I forgot to put C'!
Is that the only mistake i got?
 
  • #4
35,135
6,884


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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