Chapter 1.5, Problem 46E

Consider the function $f\left(x\right)=\tan \frac{1}{x}$.

(a) Show that $f\left(x\right)=0$ for $x=\frac{1}{\pi },\frac{1}{2\pi },\frac{1}{3\pi },\mathrm{...}$

(b) Show that $f\left(x\right)=1$ for $x=\frac{1}{\pi },\frac{1}{2\pi },\frac{1}{3\pi },\mathrm{...}$

(c) What can you conclude about $\underset{x\to 0^{+}}{\lim }\tan \frac{1}{x}$?