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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