# Taylor Approximation

Gold Member

## Homework Statement

Show that $$∫f'(x)dx/f(x) = ln|(f(x)|+C$$ where f(x) is a differential function.

## Homework Equations

First order Taylor approximation? $$f(x)=f(a)+f'(a)(x-a)$$

## The Attempt at a Solution

Well, I'm not really sure how to approach the question. It's my Numerical Methods homework, so I think I have to do it by using Taylor approximation. By applying the first order Taylor approximation I get:

$$ln|f(x)|=y, ln|f(a)| - ln|(f(x)| = (a-x)f'(x)/f(x)$$

$$ln|(f(a)/f(x)| = (a-x)f'(x)/f(x)$$

I'm kind of stuck here. Am I right in thinking that Taylor approximation is an appropriate way to approach the question?

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

Show that $$∫f'(x)dx/f(x) = ln|(f(x)|+C$$ where f(x) is a differential function.

## Homework Equations

First order Taylor approximation? $$f(x)=f(a)+f'(a)(x-a)$$

## The Attempt at a Solution

Well, I'm not really sure how to approach the question. It's my Numerical Methods homework, so I think I have to do it by using Taylor approximation. By applying the first order Taylor approximation I get:

$$ln|f(x)|=y, ln|f(a)| - ln|(f(x)| = (a-x)f'(x)/f(x)$$

$$ln|(f(a)/f(x)| = (a-x)f'(x)/f(x)$$

I'm kind of stuck here. Am I right in thinking that Taylor approximation is an appropriate way to approach the question?

Start again: you are on the wrong track.

1 person
Gold Member
Hi Ray, thanks for the reply. Would you mind giving me a hint? I really haven't a clue about the right track.

Why not take the derivative of the right-hand side?

1 person
Gold Member
Why not take the derivative of the right-hand side?

I guess my teacher wants us to solve it by the difficult way, i.e using appropriate ways.

Ray Vickson