Section 14.3

One-sided Limits;

Continuous Functions

OBJECTIVE 1

11 1

For the function

1 if 1

0 if 1

3 if 1

find: (a) lim (b) lim (c) limxx x

x x

f x x

x x

f x f x

OBJECTIVE 2

2

1

4

xR x

x

(b) Use limits to analyze the graph near any discontinuities.

Determine the numbers at which the following function is continuous.

if 0

if 0 4

1 if 4

x x

f x x x

x