Limits at Infinity

1
Limits at Infinity

• Section 3.5

2
Horizontal Asymptotes

• The line y L is a horizontal asymptote of the
  graph of f if

3
Example
Check out TABLE on calculator.

4
Limits at Infinity

• If r is a positive rational number and c is any
  real number c, then .
• Furthermore, if xr is defined for x lt 0, then
  
• .

5
Examples

Strategy Divide each term of the numerator and
denominator by the highest power of x in the
denominator.
6
Examples

7
Examples

8
Limits at Infinity

• Guidelines for finding limits at infinity of
  rational functions
• If degree of numerator is less than degree of
  denominator, the limit is zero.
• If degree of numerator is equal to degree of
  denominator, the limit is the ratio of the
  leading coefficients.
• If degree of numerator is greater than degree of
  denominator, the limit does not exist.

9
End Behavior

• End behavior of the graph of functions
• What does graph do as
  ?
• Example Describe end behavior of

10
End Behavior

• Example Describe end behavior of

11
Homework
Section 3.5 page 205 1, 3-8 all, 17, 21-25 odd,
Full curve sketches for 55, 59, 65, 67