1. The problem statement, all variables and given/known data
Show that [tex]∫f'(x)dx/f(x) = ln|(f(x)|+C[/tex] where f(x) is a differential function.
2. Relevant equations
First order Taylor approximation? [tex]f(x)=f(a)+f'(a)(x-a)[/tex]
3. 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:
[tex]ln|f(x)|=y, ln|f(a)| - ln|(f(x)| = (a-x)f'(x)/f(x)[/tex]
[tex]ln|(f(a)/f(x)| = (a-x)f'(x)/f(x)[/tex]
I'm kind of stuck here. Am I right in thinking that Taylor approximation is an appropriate way to approach the question?
Show that [tex]∫f'(x)dx/f(x) = ln|(f(x)|+C[/tex] where f(x) is a differential function.
2. Relevant equations
First order Taylor approximation? [tex]f(x)=f(a)+f'(a)(x-a)[/tex]
3. 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:
[tex]ln|f(x)|=y, ln|f(a)| - ln|(f(x)| = (a-x)f'(x)/f(x)[/tex]
[tex]ln|(f(a)/f(x)| = (a-x)f'(x)/f(x)[/tex]
I'm kind of stuck here. Am I right in thinking that Taylor approximation is an appropriate way to approach the question?
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