Chapter 2.3, Problem 56E

Let $f(x)=〚\cos x〛,-\pi \le x\le \pi .$

(a) Sketch the graph of f.

(b) Evaluate each limit, if it exists.

(i) $\underset{x\to 0}{\lim }f(x)$

(ii) $\underset{x\to {(\pi /2)}^{-}}{\lim }f(x)$

(iii) $\underset{x\to {(\pi /2)}^{+}}{\lim }f(x)$

(iv) $\underset{x\to (\pi /2)}{\lim }f(x)$

(c) For what values of a does lim _x→0 f(x) exist ?