Answer
If $f$ is continuous at $x=c,$ then, by definition, $\lim _{x \rightarrow c} f(x)=f(c)$.
Work Step by Step
In other words, the limit of a continuous function at $x=c$ is the value of the function at $x=c .$ The "simplify and plug-in" strategy is based on simplifying a function which is indeterminate to a continuous function. Once the simplification has been made, the limit of the remaining continuous function is obtained by evaluation.
