b. At the tangentline is horizontaland thus has slopeof
c. Manydifferentexamples;for instance,a polynomialfunctionsuchas
- Slopetendstoward
b.
c. ,
d.
- b.
d.
- b. The graphdropsbelowthe x-axisinto the third quadrant.Hencewe are not findingthe area belowthe
curvebut actuallythe area betweenthe curveand the x-axis.But note that the curveis symmetricabout
the origin.Hencethe regionfrom to will havethe samearea as the regionfrom to - m/sec.
FindingLimits
LearningObjectives
A studentwill be able to:
- Find the limit of a functionnumerically.
- Find the limit of a functionusinga graph.
- Identifycaseswhenlimitsdo not exist.
- Use the formaldefinitionof a limit to solvelimit problems.
Introduction
In this lessonwe will continueour discussionof the limitingprocesswe introducedin Lesson1.4. We will
examinenumericaland graphicaltechniquesto find limitswherethey existand also to examineexamples
wherelimitsdo not exist.We will concludethe lessonwith a moreprecisedefinitionof limits.
Let’s start with the notationthat we will use to denotelimits.We indicatethe limit of a functionas the
valuesapproacha particularvalueof say as
So, in the examplefrom Lesson1.3 concerningthe function we took pointsthat got closerto
the pointon the graph and observedthe sequenceof slopevaluesof the correspondingsecantlines.
Usingour limit notationhere,we wouldwrite