AP Calculus September 13, 2016 Mrs. Agnew

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Presentation transcript:

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

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

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.

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

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

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

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

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