Chapter 1.2, Problem 21E

Solution

To find: tell whether it is removable or nonremovable.

It is non-removable.

Given information: 

The function $g\left(x\right)=\frac{3}{x}$ .

Calculation:

The function has a point of discontinuity at $x=0$ .

It is an infinite discontinuity, and therefore it is non removable.

Graph of $g\left(x\right)=\frac{3}{x}$ .

Let $y=g\left(x\right)$ .

Create the table

x	$0$	$1$	-1	$-2$	$2$	$5$
y	$\infty$	$3$	$-3$	$-1.5$	1.5	$0.6$

Plot the graph according to table

  

Hence, it is non removable.