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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
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