Chapter 3, Problem 54RE

(a) Under what conditions will a limit of the form

$\underset{x\to a}{\lim }\left[f\left(x\right)/g\left(x\right)\right]$

be an indeterminate form?

(b) If ${\lim }_{x\to a}f\left(x\right)=0$ , must ${\lim }_{x\to a}\left[f\left(x\right)/g\left(x\right)\right]$ be an indeterminate form? Give some examples to support your answer