Textbook Problem

Given that

$\begin{array}{l}\underset{x\to 2}{\lim }f(x)=4\\ \underset{x\to 2}{\lim }g(x)=-2\\ \underset{x\to 2}{\lim }h(x)=0\end{array}$

find the limits that ex.ist. If the limit does not exist, explain why.

(a) $\underset{x\to 2}{\lim }[f(x)+5g(x)]$

(b) $\underset{x\to 2}{\lim }{[g(x)]}^3$

(c) $\underset{x\to 2}{\lim }\sqrt{f(x)}$

(d) $\underset{x\to 2}{\lim }\frac{3f(x)}{g(x)}$

(e) $\underset{x\to 2}{\lim }\frac{g(x)}{f(x)}$

(f) $\underset{x\to 2}{\lim }\frac{g(x)}{f(x)}$