c.
d. doesnot exist.
- a.
b. doesnot exist.
c. is somenumbercloseto 1 and less than 1, but not equalto 1.
d. is somenumbercloseto 1 and less than 1, but not equalto 1.
- The limit doesexist.This can be verifiedby usingtheTRACEorTABLEfunctionof your calculator, applied
toxvaluesvery closetox= 2. - The limit doesexist.This can be verifiedby usingtheTRACEorTABLEfunctionof your calculator, applied
toxvaluesvery closetox= -1. - The limit doesexist.This can be verifiedby usingtheTRACEorTABLEfunctionof your calculator, applied
toxvaluesvery closetox= 2. - The limit doesexist.This can be verifiedwith eithertheTRACEorTABLEfunctionof your calculator.
- The limit doesnot exist;ZOOMin on the grapharound and see that they-valuesapproacha
differentvaluewhenapproachedfrom the right and from the left.
EvaluatingLimits
LearningObjectives
A studentwill be able to:
- Find the limit of basicfunctions.
- Use propertiesof limitsto find limitsof polynomial,rationaland radicalfunctions.
- Find limitsof compositefunctions.
- Find limitsof trigonometricfunctions.
- Use the SqueezeTheoremto find limits.
Introduction
In this lessonwe will continueour discussionof limitsand focuson waysto evaluatelimits.We will observe
the limitsof a few basicfunctionsand then introducea set of laws for workingwith limits.We will conclude
the lessonwith a theoremthat will allowus to use an indirectmethodto find the limit of a function.
DirectSubstitutionand BasicLimits
Let’s beginwith someobservationsaboutlimitsof basicfunctions.Considerthe followinglimit problems: