Question

How do you apply taylor's formula on lnx??? Knowing that x0 = 0 and that Pn(x)=f(x0)+f'(x0)(x-x0)+1/2!f''(x0)(x-x0)2+1/3!f'''(x0)(x-x0)3+....+1/n!f(n)(x0)(x-x0)n

Answer 1

look it up ;DDD

Answer 2

I think I would expand around x0= 1 where ln(1)=0
if you use x0 = 0, ln(0) is undefined (or negative infinity)

second, you need to find the derivatives of ln(x)
first derivative: 1/x
2nd derivative: -1/x^2
3rd : 2/x^3
keep going until you see a pattern

next, (assuming we expand around x0=1)
replace x with 1 and simplify all the derivatives to a number

use those numbers in the taylor series expansion

Answer 3

http://math.stackexchange.com/questions/458511/type-of-singularity-of-log-z-at-z-0

Answer 4

the Laurent series is more general form of Taylor series. That post on M.SE says that no Laurent series exist for log(z) centered at zero ... I suppose no Taylor series for log(x) about x=0.

Answer 5

Thank you so much for all of your answers