Math 121

Section 1.5

Limits

Example of limits

Find the limit:

Find the limit of the function as x approaches 1

x	.9	.99	.999	1.1	1.01	1.001
	1.810	1.980	1.998	2.210	2.020	2.002

Value in the table seem to approach 2 as x approaches 1

Definition:

Thus,

Examples:

1) Find

2) Find

3) Find

Limit does not exist

4) Find (Limit does not exist)

5) find

In example 5, if you substitute 3 in for x before you reduce the polynomial down, you will get an undetermined form.

Example from the textbook

Page 60

40)

42)

34)

Evaluating a limit from a graph

Example 1

1) Find

2) Find

3) Find Left hand limit (The y value x approaches from the left)

4) Find Right hand limit (The y value x approaches from the right)

5) Find The limit doesn’t exist since the right hand and the left hand limits are different.

Example 2

1) Find No Limit

2) Find

3) Find