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AP Calculus AB
Chapter 2: Limits & Continuity
Lesson 2.2:
Limits
Involving
Infinity
Example 1
Example 3
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Example 5
Find the vertical asymptotes of f(x)
For very large values of x, we can sometimes model the behavior of a
complicated function by a simpler one that acts in basically the same way.
End Behavior Models for Limits as x
approaches +/- infinity:
Consider the polynomial
An end behavior model
for this function:
Review: Finding Asymptotes Using Limits
Horizontal:
Vertical:
Scenario #1: Degree is greater in numerator.
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Scenario #2: Degree is greater in denominator.
Scenario #3: Degree of numerator equals degree of denominator.
Let
Show
Let
Show
is a Left End Behavior Model for f(x).
is a Right End Behavior Model for f(x).