Q. 3 - Calculus

Question

If $f$ is a continuous function, what can you say about $\underset{x\to 1}{\lim }f\left(x\right)?$

Step-by-Step Solution

Answer

It can be concluded that there is no hole in the graph of the function at$x=c.$

Step 1. Given Information.

A continuous function is given.

Step 2. Conclusion.

A function $f$ is continuous at $x=c$ whenever $f\left(c\right)$ is defined, $f$ has a limit as $x\to c$ and the value of the limit and the value of the function agree. This guarantees that there is not a hole or jump in the graph of $f$at $x=c.$