Write the Maclaurin series expansion of the function $\log \left(1-x\right) ; -1\le x\le 1$.

Write the Maclaurin series expansion of the following function ${\tan }^{-1}\left(x\right) ;-1\le x\le 1$.

Evaluate the following limit, if necessary use L'Hospital Rule $\underset{x\to 0}{\lim }\frac{1-\cos \left(x\right)}{x^2}$.

Evaluate $\underset{x\to \infty }{\lim }\frac{2x^2-3}{x^2-5x+3}$, if necessary use L’Hospital Rule.

Evaluate $\underset{x\to \infty }{\lim }\frac{x}{\log \left(x\right)}$, if necessary use L’Hôpital Rule.