Chapter 15, Problem 1SGA

To determine

To Justify: The given statement.

Answer to Problem 1SGA

False

Explanation of Solution

Given:

  $f\left(a\right)and\underset{x\to a}{\lim }f\left(x\right)\text{ are the same}\text{.}$

  $\begin{array}{l}f\left(a\right)and\underset{x\to a}{\lim }f\left(x\right)\text{ are the same}\text{.}\\ \text{The given statement is false because}\\ f\left(a\right)=\underset{x\to a}{\lim }f\left(x\right)\text{ will be satisfied only when the function will continuous at }x=a\\ \text{but if the function will discontinuous at }x=a\text{ then }f\left(a\right)\ne \underset{x\to a}{\lim }f\left(x\right)\end{array}$