Chapter 8.7, Problem 45E

(a)

To determine

The type of indeterminate form (if any) that is obtained by direct substitution for the expression $\underset{x\to \infty }{\lim }x\sin \left(\frac{1}{x}\right)$.

(b)

To determine

To calculate: The provided limit $\underset{x\to \infty }{\lim }x\sin \left(\frac{1}{x}\right)$ using L’Hopital’s rule if necessary.

(c)

To determine

To graph: The provided function $f\left(x\right)=x\sin \left(\frac{1}{x}\right)$.