Recallalso that we foundthat the slopevaluestendedto the value ; henceusingour notationwe
can write
FindingLimitsNumerically
In our examplein Lesson1.3 we usedthis approachto find that. Let’s applythis technique
to a morecomplicatedfunction.
Considerthe rationalfunction. Let’s find the followinglimit:
.Unlikeour simplequadraticfunction, it is tediousto computethe pointsmanually. So let’s use
theTABLEfunctionof our calculator. Enterthe equationin your calculatorand examinethe tableof points
of the function.Do you noticeanythingunusualaboutthe points?(Answer:Thereare errorreadingsin-
dicatedfor
becausethe functionis not definedat thesevalues.)
Eventhoughthe functionis not definedat we can still use the calculatorto read the -values
for valuesvery closeto Press2ND [TBLSET]and setTblstartto and to (see
screenon left below).The resultingtableappearsin the middlebelow.
Can you guessthe valueof? If you guessed you wouldbe correct.
Beforewe finalizeour answer, let’s get evencloserto and determineits functionvalueusingthe
CALCVALUEtool.
Press2ND[TBLSET]and changeIndpntfromAutoto Ask. Nowwhenyou go to the table,enter
and press[ENTER]and you will see the screenon the right above.Press[ENTER]and
see that the functionvalueis whichis the closestthe calculatorcan displayin the four decimal