1. AP Calculus September 13, 2016 Mrs. Agnew
Infinite Limits
AP Calculus
September 13, 2016
Mrs. Agnew

2. Essential Stuff Question How do you evaluate infinite limits?
Vocabulary
Infinite Limit
Horizontal Asymptote
Vertical Asymptote

3. Infinite Limits What does the notation below mean?
Note that ∞ is not a number. It is a notation to helps us identify why the limit does not exist.

4. Vertical Asymptotes Examples
The line x = c is a vertical asymptote if the limit of the function is ±∞ as x approaches c from the left, right, or both.
Vertical asymptotes are “problems” in the denominator.
Examples

5. Limits at Infinity What does the notation below mean?
Find the following limit numerically.

6. Horizontal Asymptotes
The line y = L is a horizontal asymptote if:
The horizontal asymptote of a function is the y value that the graph “levels off” at L as the x values get much bigger/smaller.
Examples

7. Horizontal Asymptotes
Three rules regarding HA:
If bigger exponent is on top, the limit is infinity.
If bigger exponent is on bottom, the limit is zero.
If exponents top and bottom are the same, the limit is the ratio of the coefficients.
Examples

8. Homework:
page 88 – 90
#13 – 31 (Odd), 37 – 53 (Odd), 64, 67, 68