Textbook Problem

(a) If the symbol $〚〛$ denotes the greatest integer function defined in Example I 0, evaluate

(i) $\underset{x\to 2^{+}}{\lim }〚x〛$

(ii) $\underset{x\to -2}{\lim }〚x〛$

(iii) $\underset{x\to 2.4}{\lim }〚x〛$

(b) If n is an integer, evaluate

(i) $\underset{x\to n-}{\lim }〚x〛$

(ii) $\underset{x\to n^{+}}{\lim }〚x〛$

(c) For what values of a does $\underset{x\to 0}{\lim }〚x〛$ exist?