Chapter 1.6, Problem 53E

 (a) If the symbol $〚〛$ denotes the greatest integer function defined in Example 10, 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 a integer, evaluate

(i) $\underset{x\to n^{-}}{\lim }〚x〛$

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

(c) For what values of a does ${\lim }_{x\to a}〚x〛$ exists?