3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

To Infinity and Beyond

By the end of this lesson, Buzz Light Year will be able to:

1.) Determine whether a function approaches infinity.

2.) Find vertical/horizontal asymptotes of functions.

3.) Understand the properties of infinite limits.

4.) Evaluate the limit of a function as x approaches infinity.

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Solutions to Evaluating Limits

1.)

2.)

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Infinite Limit

A function in which y increases or decreases without

bound as x approaches c is said to have an infinite limit.

Take a look at WS6--Limits: A Graphical Approach!

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Ex. 1) Evaluate the limit as x approaches two of

x 1.5 1.9 1.99 1.999 2.001 2.01 2.1 2.5

f(x)

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Ex. 2) Use a graphing calculator to determine the limit

of the following functions.

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Infinite limit = Vertical asymptote

If y approaches as x approaches c from the

right or left, then the line x=c is a vertical asymptote.

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Ex. 3) Determine all vertical asymptotes of the graph

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Properties of Infinite Limits

Let c and L be real numbers and f and g be functions such

that

1.) Sum or difference

2.) Product

3.) Quotient

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Ex. 4) Evaluate the limits, using properties where applicable.

a.)

b.)

c.)

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Limits at Infinity vs. Infinite Limits

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Limits at Infinity

Ex. 5) Use the table below to evaluate the limit.

x -100 -10 -1 0 1 10 100

f(x) -2.997 -2.97 1.5 0 1.5 2.97 2.9997

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Ex. 6) Find the limit.

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Limits at infinity = Horizontal asymptote

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

#

##

#

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Ex. 7 Find the limit.

3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014

Homework

Page 84 Exercises 1-4,25-44

Page 193 Exercises 1-6, 11-20