Problem

1. (10 points) Find the following limits:

(a) (5 points) $\lim_{x \to 0} \dfrac{2^x-1}{4^x-1}$.

(b) (5 points) $\lim_{x \to 0} \sin^{-1}\left(\dfrac{1-x}{1-x^2}\right)$, where $\sin^{-1}$ is the inverse function of sine.