Chapter 1.6, Problem 43ES

In parts (a)-(c), find the limit by making the indicated substitution.

(a) $\underset{x\to +\infty }{\lim }x\sin \frac{1}{x};t=\frac{1}{x}$

(b) $\underset{x\to -\infty }{\lim }x\left(1-\cos \frac{1}{x}\right);t=\frac{1}{x}$

(c) $\underset{x\to \pi }{\lim }\frac{\pi -x}{\sin x};t=\pi -x$