Matt Wolf - Central Bucks School District
|Learning Goals: |At the completion of the lesson, you will be able to… |
| |Evaluate infinite limits of polynomial and rational functions |
| |Evaluate limits that are equal to infinity or negative infinity |
Online Video:
As x gets increasingly large we say it approaches infinity (∞) and we write: [pic]
As x gets extremely small we say it approaches negative infinity (-∞) and write: [pic]
Evaluating Infinite Limits of Rational Functions
To calculate the infinite limit of a rational function [pic], examine the following cases:
Example: Evaluate the following infinite limit. [pic]
Example: Evaluate the following infinite limit. [pic]
Example: Evaluate the following infinite limit. [pic]
Evaluating Limits Equal to Infinity
To evaluate limits equal to infinity we analyze the behavior of the Reciprocal Function:
[pic] [pic]
Examples: Evaluate the following limits.
[pic] [pic] [pic]
[pic] [pic] [pic]
[pic]= [pic]= [pic]=
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Case 1: If the degree of the numerator is less than the degree of the denominator then [pic].
Case 2: If the degree of the numerator is the same as the degree of the denominator then [pic] where a is the leading coefficient of f(x) and b is the leading coefficient of g(x)
Case 3: If the degree of the numerator is greater than the degree of the denominator then
[pic]
if [pic]is positive if [pic] is negative
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