Chapter 14.3, Problem 9AYU

In Problems 7-42, find each limit algebraically.

If $\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$, then $f$ is ________ at ________________.

To determine

To fill: If $\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$, then $f$ is ______________ at _____.

Answer to Problem 9AYU

‘Continuous at $c$’.

Explanation of Solution

If the limit of $f\left(x\right)$ as $x$ approaches to $c$ is equal to the functional value of $f\left(x\right)$ at $c$, then by definition of continuity of $f$ we can say that, if $\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$, then $f$ is continuous at $c$.