CK12 Calculus - Single Variable

• Examineinfinitelimitsat infinity.

Introduction
In this lessonwe will returnto the topicsof infinitelimitsand end behaviorof functionsand introducea new
methodthat we can use to determinelimitsthat haveindeterminateforms.
ExamineEnd Behaviorof Functionson InfiniteIntervals
Supposewe are tryingto analyzethe end behaviorof rationalfunctions.In Lessonon InfiniteLimitswe
looked at some rational functions such as and showed that and

. We requiredan analysisof the end behaviorof sincecomputingthe limit by direct
substitutionyieldedthe indeterminateform. Our approachto computethe infinitelimit was to look at
actualvaluesof the function as approached. We interpretedthe resultgraphicallyas the
functionhavinga horizontalasymptoteat

We werethen able to find infinitelimitsof morecomplicatedrationalfunctionssuchas

usingthe fact that. Similarly, we usedsuchan approachto
computelimitswheneverdirectsubstitutionresultedin the indeterminateform , suchas.

Now let’s considerotherfunctionsof the form wherewe get the indeterminateforms and
and determinean appropriateanalyticalmethodfor computingthe limits.
Example1:

Considerthe function and supposewe wish to find and We note
the following:
1.Directsubstitutionleadsto the indeterminateforms and

2. The functionin the numeratoris not a polynomialfunction,so we cannotuse our previousmethodssuch
   as applying