Chapter 14, Problem 26RE

To determine

To find: The function continuous or not at 0.

Answer to Problem 26RE

f is not continuous at 0.

Explanation of Solution

Given information:

  

For continuous

  $\underset{x\to 0}{\lim }f(x)=f(0)$

Now,

  $\begin{array}{l}\underset{x\to 0^{+}}{\lim }f(x)=1\\ \underset{x\to 0^{-}}{\lim }f(x)=4\end{array}$

So, $\underset{x\to 0^{+}}{\lim }f(x)\ne \underset{x\to 0^{-}}{\lim }f(x)$

Hence, The limit do;t exist

So, f is not continuous at $x=0$

Hence, f is not continuous at 0