CK12 Calculus - Single Variable
NormalProbabilities If you weretold by the postalservicethat you will receivethe packagethat you havebeenwaitingfor sometimetomo ...
Figure 25 where is calledthe probabilitydensityfunction (pdf).One of the mostusefulprobabilitydensity functionsis thenormalcurve ...
wherethe factor is calledthenormalizationconstant.It is neededto makethe probabilityover the entirespaceequalto That is, Example ...
TechnologyNote:To makethis computationwith a graphingcalculatorof the TI-83/84family, do the fol- lowing: FromtheDISTRmenu(Figu ...
Example8: An IntelligenceQuotientor IQ is a scorederivedfrom differentstandardizedtestsattemptingto measure the levelof intellig ...
Integratingnumerically, we get So the probabilityof selectingat randoma personwith an IQ scoreabove is That’s aboutone personin ...
where is the initialdisplacementof the spring( if the springis initiallyunstretched)and is the final displacement.A forceof is e ...
(b) Whatis the probabilitythat a customerhas to wait morethan minutes? The averageheightof an adultfemalein Los Angelesis inche ...
6. TranscendentalFunctions...................................................................................................... ...
Example1: Determinewhetherthe functionsare one-to-one:(a) (b) Solution: It is best to graphboth functionsand drawon eacha horizo ...
The Inverseof a Function We discussedabovethe conditionfor a one-to-onefunction:for eachoutput,thereis only one input.A one- to- ...
and and are inversesof eachother. Note:In general, Whenis a functioninvertable?It is interestingto note that if a function is al ...
Replacing whichis the inverseof the originalfunction. Graphsof InverseFunctions Whatis the relationshipbetweenthe graphsof and? ...
that is continuousfor all The inverseof is whereits domainis all and its rangeis We concludethat if is a functionwith domain and ...
Since differentiatingimplicitly, Solvingfor we finallyobtain whichis the sameresult. ReviewQuestions In problems#1–3,find the in ...
9. 10. Answers Functionhas an inverse. Functiondoesnot havean inverse. Functiondoesnot havean inverse. o ...
or The graphbelowshowsthe two basicshapes: LogarithmicFunctions Recallfrom your previouscoursesin algebrathat a logarithmis an e ...
We denotethe naturallogarithmof by ratherthan So keepin mind,that is the power to which mustbe raisedto produce That is, the fol ...
Similarly, in the specialcasewhenthe base the two equationsabovetake the forms and The graphbelowshowsthis relationship: Beforew ...
The function is equivalentto if and The function is equivalentto if and You shouldalso recallthe followingimportantpropertiesa ...
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