Chapter 14, Problem 11CT

To determine

T find: The left limit of $y=f(x)$ exist or not.

Answer to Problem 11CT

  $\underset{x\to 1}{\lim }f(x)=2$

Explanation of Solution

Given information:

  

At first we find the right limit :

Here , $\underset{x\to 1^{+}}{\lim }f(x)=2$

Left limit

  $\underset{x\to 1^{-}}{\lim }f(x)=2$

[as same from left limit]

  $\underset{x\to 1^{+}}{\lim }f(x)=\underset{x\to 1^{-}}{\lim }f(x)=2$

Hence, limit exists

And

  $\underset{x\to 1}{\lim }f(x)=2$