Chapter 14.1, Problem 39AYU

In Problems 23-42, graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x\to 0}{\lim }f\left(x\right),f\left(x\right)\text{ = }\{\begin{array}{l}x\text{ if }x\text{ < 0}\\ 1\text{ if }x\text{ = 0}\\ 3x\text{ if }x\text{ > 0}\end{array}$

To determine

To find: Graph of each function. Use the graph to find the indicated limit, if it exists.

Answer to Problem 39AYU

Solution:

$\underset{x \to 0}{\text{lim}}f(x) = 0$

Explanation of Solution

Given:

$\underset{x \to 0}{\text{lim}}f(x), f(x) = \{\begin{array}{c}x\text{ if }x < 0\\ 1\text{ if }x = 0\\ 3x\text{ if }x > 0\end{array}$

$\underset{x \to 0}{\text{lim}}f(x) = 0$