Chapter 1.5, Problem 33ES

A function $f$ is said to have a removable discontinuity at $x=c$ if ${\lim }_{x\to c}f\left(x\right)$ exists but $f$ is not continuous at $x=c,$ either because $f$ is not defined at $c$ or because the definition for $f\left(c\right)$ differs from the value of the limit. This terminology will be needed in these exercises.

(a) Sketch the graph of a function with a removable dis continuity at $x=c$ for which $f\left(c\right)$ is undefined.

(b) Sketch the graph of a function with a removable discontinuity at $x=c$ for which $f\left(c\right)$ is defined.