Question

$If\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right),thenfis\_\_\_\_\_\_at\_\_.$

Short answer

continuous, c

Step-by-step solution

Step. 1 Given 

It is given that, $\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$.

Step. 2 Conclusion of f(x)

Since the limit $\underset{x\to c}{\lim }f\left(x\right)$exist and is equal to $f\left(c\right)$then it means $f\left(x\right)$is continuous at $x=c$.

Therefore, in the blanks if $\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$then $f$ is continuousat $c$.