placesallottedin the table.So our guessis correctand.
FindingLimitsGraphically
Let’s continuewith the sameproblembut now let’s focuson usingthe graphof the functionto determineits
limit.
We enterthe functionin the menuand sketchthe graph.Sincewe are interestedin the valueof the
functionfor closeto we will look toZOOMin on the graphat that point.
Our graphaboveis set to the normalviewingwindow Hencethe valuesof the functionappear
to be verycloseto 0. But in our numericalexample,we foundthat the functionvaluesapproached
To see this graphically, we can use theZOOMandTRACEfunctionof our calculator.
Beginby choosing[ZOOM]functionand choose[BOX]. Usingthe directionalarrowsto movethe cursor,
makea box aroundthe value (Seethe screenon the left belowPress[ENTER]and[TRACE]and
you will see the screenin the middlebelow.) InTRACEmode,type the number and press
[ENTER]. You will see a screenlike the one on the right below.
The graphingcalculatorwill allowus to calculatelimitsgraphically, providedthat we havethe functionrule
for the functionso that we can enterits equationinto the calculator. Whatif we haveonly a graphgivento
us and we are askedto find certainlimits?
It turnsout that we will needto haveprettyaccurategraphsthat includesufficientdetailaboutthe location
of data points.Considerthe followingexample.
Example1:
Find for the functionpicturedhere.Assumeunitsof value1 for eachunit on the axes.