## xartaan 3 years ago Taylor Series question here: So I am learning about Taylor series/polynomials and I am deriving some of the common functions just to get comfortable with the process. My problem is with ln(x). My process for finding taylor polynomials has been to take a few derivatives so in this case $f(x)=\ln(x)....f'(x)=\frac{ 1 }{ x }...f''(x)=\frac{ -1 }{ x^2 }....f'''(x)=\frac{ 2 }{ x^3 }$ etc... But for the next step I have been evaluating each term at x=0 to find the general term. How can I do this for ln(x) since as far as I know, ln(0) isn't valid? (at least at my level of maths)

1. satellite73

$\ln(x)$ therefore has no taylor series expansion at $$x=0$$

2. TuringTest

You don't take the taylor series of lnx about x=0 for the reason you discovered. It's much more common to take it around x=-1, or expand ln(x+1)

3. satellite73

as you can see every term will be undefined you can expand at 1 say

4. satellite73

what @TuringTest said

5. xartaan

Ok I will try from a different x then. I guess my confusion was just about finding a general term. I will expand at a different point and see if I can get it.

6. xartaan

Aha! That worked perfectly! Substituting x=1. Thanks guys!

Find more explanations on OpenStudy