Chapter 4.4, Problem 2E

Given that

$\begin{array}{c}\underset{x\to a}{\lim }f(x)=0\underset{x\to a}{\lim }g(x)=0\underset{x\to a}{\lim }h(x)=1\\ \underset{x\to a}{\lim }p(x)=\infty \underset{x\to a}{\lim }q(x)=\infty \end{array}$

which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible.

(a) $\underset{x\to a}{\lim }[f(x)p(x)]$

(b) $\underset{x\to a}{\lim }[h(x)p(x)]$

(c) $\underset{x\to a}{\lim }[p(x)q(x)]$