We needto showthat for eachopenintervalof 7, we can find an openneighborhoodof 3, that doesnot include
3, so that allxin the openneighborhoodmap into the openintervalof 7.
Equivalently, we mustshowthat for everyintervalof say we can find an intervalof ,
say suchthat whenever
The first inequalityis equivalentto and solvingfor we have
Henceif we take , we will have
Fortunately, we do not haveto do this to evaluatelimits.In Lesson1.6 we will learnseveralrulesthat will
makethe task manageable.
LessonSummary
- We learnedto find the limit of a functionnumerically.
- We learnedto find the limit of a functionusinga graph.
- We identifiedcaseswhenlimitsdo not exist.
- We usedthe formaldefinitionof a limit to solvelimit problems.
ReviewQuestions - Use a tableof valuesto find.
a.Use -valuesof b.Whatvaluedoesthesequence
of valuesapproach?
- Use a tableof valuesto find.
a. Use -valuesof
b. Whatvaluedoesthe sequenceof valuesapproach?
- Considerthe function Generatethe graphofp(x) usingyour calculator. Find eachof
the followinglimitsif they exist.Use tableswith appropriatexvaluesto determinethe limits.
a.
b.