### Home > PC3 > Chapter Ch8 > Lesson 8.3.2 > Problem8-105

8-105.

Let $f ( x ) = \left\{ \begin{array} { l l } { 2 ^ { x } } & { \text { for } x < 2 } \\ { 4 } & { \text { for } x \geq 2 } \end{array} \right.$. Evaluate:

1. $\lim\limits_{ x \rightarrow 2 } f ( x )$

The limit must approach the same height from both sides in order to exist.

1. $\lim\limits_{ x \rightarrow 5 } f ( x )$

Which piece of the function should you use?

1. Is the function continuous at $x = 2$? Use the formal definition of continuity to justify your answer.

For a function to be continuous at a point, the one-sided limits must agree and they must equal the value of the function at that point.

2. Is the function continuous at $x = 5$? Use the formal definition of continuity to justify your answer.