CK12 Calculus - Single Variable
b. In whatyear will you tripleyour originalamount? Supposethat in the previousproblem,you startedwith but maintainedthe sameint ...
The data suggestthat womenwill reach in 2009;this is unrealisticbasedon currentreportsthat womenstill lag far behindmen in equa ...
Supposewe magnifyour pictureand zoomin on the point The picturemightlook like this: We note that the curvenow looksvery muchlike ...
of usingthe function ; hence Recallthat for pointsvery closeto the points on the line are closeapproximatepointsof the function. ...
This processof findinghow functionvaluesbehaveas we systematicallyget closerand closerto partic- ular -valuesis the processof fi ...
The averagevelocityof a fallingobjectfrom to is givenby HW Problem#10 will give you an opportunityto explorethis relationship.In ...
We now will constructfour rectanglesthat will serveas the basisfor our approximationof the area.The subintervalswill serveas the ...
and Notethat this approximationis very closeto our initialapproximationof However, sincewe took the maximumvalueof the functionf ...
We havenot yet developedany computationalmachineryfor computing derivatives and integrals so we will just stateone popularapplic ...
d. For whatvaluesof do the tangentlines appearto havenegativeslope? The cost of producing Hi-Fi stereoreceiversby Yamahaeachwee ...
b. At the tangentline is horizontaland thus has slopeof c. Manydifferentexamples;for instance,a polynomialfunctionsuchas Slopet ...
Recallalso that we foundthat the slopevaluestendedto the value ; henceusingour notationwe can write FindingLimitsNumerically In ...
placesallottedin the table.So our guessis correctand. FindingLimitsGraphically Let’s continuewith the sameproblembut now let’s f ...
By inspection,we see that as we approachthe value from the left, we do so alongwhatappearsto be a portionof the horizontalline W ...
numbersas we get closeto Alternatively, for we see that the pointsall lie in the fourth quadrantand decreaseto largenegativenumb ...
We needto showthat for eachopenintervalof 7, we can find an openneighborhoodof 3, that doesnot include 3, so that allxin the ope ...
c. d. Find the valuesof the functioncorrespondingto How do thesefunctionvaluescompare to the limitsyou foundin a–c?Explainyour a ...
b. c. d. In problems#6–8,determineif the indicatedlimit exists.Providea numericalargumentto justifyyour answer. In pro ...
c. d. doesnot exist. a. b. doesnot exist. c. is somenumbercloseto 1 and less than 1, but not equalto 1. d. is somenumbercloset ...
Theseare examplesof limitsof basicconstantand linearfunctions, and We note that eachof thesefunctionsare definedfor all real num ...
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