Problem

1. $(7\%)(8\%)$ Find the following limits:

(1a) $\displaystyle \lim_{x\to 0}f(x)$ with $f(x)=\sin\left(\frac{1}{x}\right)I(x>0)$.

(1b) $\displaystyle \lim_{x\to\infty}x\tan\left(\frac{1}{x}\right)$.