Chapter 2.2, Problem 7E

For the function $g$ whose graph is shown, find a number $a$ that satisfies the given description.

(a) $\underset{x\to a}{\lim }g(x)$ does not exist but $g(a)$ is defined.

(b) $\underset{x\to a}{\lim }g(x)$ exists but $g(a)$ is not defined.

(c) $\underset{x\to a^{-}}{\lim }g(x)$ and $\underset{x\to a^{+}}{\lim }g(x)$ both exist but $\underset{x\to a}{\lim }g(x)$ does not exist.

(d) $\underset{x\to a^{+}}{\lim }g(x)=g(a)$ but $\underset{x\to a^{-}}{\lim }g(x)\ne g(a)$ .