### Home > CALC > Chapter 2 > Lesson 2.3.2 > Problem2-120

2-120.

For each part below, draw a graph of a function that meets the given conditions, if possible. If such a function is not possible, explain why.

1. $g(x)$ is discontinuous at $x = a$, but $\lim\limits_ { x \rightarrow a } g ( x )$ exists.

2. $g(x)$ is continuous at $x = a$, but $\lim\limits_ { x \rightarrow a } g ( x )$ does not exist.

3. $g(x)$ is discontinuous at $x = a$, and $\lim\limits_ { x \rightarrow a } g ( x )$ does not exist.

Limits exist when both sides approach the same finite value. What does it mean for a limit to not exist.