Use Taylor Series To Evaluate

[xtrubambinoxpr]

1. Homework Statement [/b]
use taylor series to evaluate lim x -> 0 of [itex]\frac{ln(x)}{(x-1)}[/itex]

Homework Equations

I know that -ln (1-x) taylor polynomial
and that of ln (1+x)

The Attempt at a Solution

Using the basics that I know I would assume I would just make ln (1+x) = ln (x) by making x = x-1

so ln (1+(x-1)) = ln x

But i don't know if that is correct

 

[LCKurtz]

1. Homework Statement [/b]
use taylor series to evaluate lim x -> 0 of [itex]\frac{ln(x)}{(x-1)}[/itex]

Homework Equations

I know that -ln (1-x) taylor polynomial
and that of ln (1+x)

The Attempt at a Solution

Using the basics that I know I would assume I would just make ln (1+x) = ln (x) by making x = x-1

so ln (1+(x-1)) = ln x

But i don't know if that is correct

Why would you need Taylor series for ##\lim_{x\to 0}##? I guess maybe you really mean ##x\to 1##, which is more interesting? If so, do what you suggest by writing the series for ##\ln(1+(x-1)## and divide by ##x-1##.

 

[xtrubambinoxpr]

Why would you need Taylor series for ##\lim_{x\to 0}##? I guess maybe you really mean ##x\to 1##, which is more interesting? If so, do what you suggest by writing the series for ##\ln(1+(x-1)## and divide by ##x-1##.

correct me if I am wrong but I got 1