Chapter 8.7, Problem 82E

To determine

The error in the provided calculation which is solved using the L’Hopital rule. The provided calculation is:

$\begin{array}{c}\underset{x\to \infty }{\lim }x\cos \frac{1}{x}=\underset{x\to \infty }{\lim }\frac{\cos \left(1/x\right)}{1/x}\\ =\underset{x\to \infty }{\lim }\frac{\left[-\sin \left(1/x\right)\left(1/x^2\right)\right]}{-1/x^2}\\ =0\end{array}$