### Home > PC3 > Chapter 7 > Lesson 7.1.5 > Problem7-61

7-61.

Let $f(x) = \left\{ \begin{array} { l } { x ^ { 2 } - 3 \quad\text {for } x \leq 2 } \\ { 5 - x \quad\ \text { for } x > 2 } \end{array} \right.$. Evaluate the following limits. If the limit does not exist, explain why it does not exist.

1. $\lim\limits _ { x \rightarrow 2 ^ { + } } f ( x )$

As $x→2$ from the right (positive) side, what height does the graph approach? Which part of the function should you use to determine your answer?

2. $\lim\limits _ { x \rightarrow 2 ^ { - } } f ( x )$

As $x→2$ from the left (negative) side, what height does the graph approach? Which part of the function should you use to determine your answer?

3. $\lim\limits _ { x \rightarrow 2 } f ( x )$

Are the limits from the left and right sides approaching the same value?