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Limits at Infinity

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Limits at Infinity Section 3.5 Horizontal Asymptotes The line y = L is a horizontal asymptote of the graph of f if Example Limits at Infinity If r is a positive ... – PowerPoint PPT presentation

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Title: 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
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