Question

Can you show me the passages for the mclaurin taylor series:

Answer 1

\[\ln \left( 1-x ^{2} \right)\]

Answer 2

How do I find the final function?

Answer 3

http://en.wikipedia.org/wiki/Taylor_series#Definition

a = 0

find the successive derivatives

Answer 4

Alternative method:
\[\ln(1-x^2)=\ln\bigg((1-x)(1+x)\bigg)=\ln(1-x)+\ln(1+x)\]
Then you can find the corresponding Taylor series (derivative computations would be simpler), or if you already know the series, you would just add them. The link dumbcow posted actually has both series listed.