Understanding Taylor Series Approximation with Taylor's Theorem Explanation

[rmc240]

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

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

 

[LCKurtz]

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

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?

 

[rmc240]

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.