Understanding Taylor Series Approximation with Taylor's Theorem Explanation

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rmc240
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I'm reading a derivation and it says that the following approximation can be used:

attachment.php?attachmentid=69764&stc=1&d=1400020033.png


I do not under stand how Taylor's theorem allows for this approximation. Can anyone explain this a little?
 

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rmc240 said:
I'm reading a derivation and it says that the following approximation can be used:

attachment.php?attachmentid=69764&stc=1&d=1400020033.png


I do not under stand how Taylor's theorem allows for this approximation. Can anyone explain this a little?

If you let ##f(r) = \frac{dv}{dr}## you have ##f(r+dr) = f(r) + f'(r)dr##. Do you recognize that?
 
Yea, my problem was realizing that I was supposed to approximate the function around r and evaluate the function at r + dr. Should have seen that. Thank you for your help.