Chapter 14, Problem 10CT

To determine

T find: The left limit of $y=f(x)$ at $x\to -2$

Answer to Problem 10CT

  $\underset{x\to -2}{\lim }f(x)=2$

Explanation of Solution

Given information:

  

At first we find the right limit :

Here , $\underset{x\to 2^{+}}{\lim }f(x)=2$ [We apporch from left to $-2$ then we get functional value 2]

Left limit

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

[as same from left limit]

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

Hence, limit exists

And

  $\underset{x\to -2}{\lim }f(x)=2$