Chapter 2.2, Problem 52E

The ceiling function For any real number x, the ceiling function ⌈x⌉ is the smallest integer greater than or equal to x.

1. a. Graph the ceiling function y = ⌈x⌉, for −2 ≤ x ≤ 3.
2. b. Evaluate $\underset{x\to 2^{-}}{\lim }\lceil x\rceil$, $\underset{x\to 1^{+}}{\lim }\lceil x\rceil$, and $\underset{x\to 1.5}{\lim }\lceil x\rceil$.
3. c. For what values of a does $\underset{x\to a}{\lim }\lceil x\rceil$ exist? Explain.