Limits Infinity

1
Limits _at_ Infinity

• Not to be confused with Infinite Limits!

2
Limits _at_ Infinity

• Infinite Limits
• Vertical Asymptotes

• Limits at Infinity
• Horizontal Asymptotes

3
Limits _at_ Infinity

• Key Idea
• Write all terms of the Rational Function as
  fractions and then consider..

0
0
0
0
0
4
Rational Functions

• Limits at Infinity
• Compare the degree of the numerator to the degree
  of the denominator

5
Rational Functions

• If the degree of the numerator is LESS THAN the
  degree of the denominator

6
Rational Functions

• If the degree of the numerator is EQUAL TO the
  degree of the denominator.

7
Rational Functions

• If the degree of the numerator is GREATER THAN
  the degree of the denominator

8
Examples