1225BW11_sol.pdf

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Department
Mathematics
Course
Mathematics 1225A/B
Professor
Jennifer Mori
Semester
Winter

Description
basedon2011testsMathematics1225BCODE111Page1Test1PracticeTestPARTA17marks3211markSimplifylne65AeB6CeD9E0a3SolutionWeknowthatforanybaseblogbaandalsothatlnxmeanslogxThereforelne3be322andsowegetlne3933222AnotherApproachSincelne3lneandlne1weseethatlne3lne319log2log84421markSimplifylog42log104AB1C4Dlog2Elog4422Solution2log2log82log28log16log44444412log4log4log4log22222231markFindtheslopeofthetangentlinetothegraphofylogxatthepointwith3x31AB1Cln3D0E3ln33ln3SolutionTheslopeofthetangentlinetothegraphofyfxatthepointwithxaisgivenbyfa1Forfxlogxwehavefxandsoweseethattheslopeofthetangentlinetothegraphof3xln31ylogxatthepointwithx3isf333ln3ln241markIffxxndfxln2ln212xA2BxCxln2DeEln2ln21SolutionWehavexraisedtoaconstantpowersoweusethepowerrulefxln2xln21xln23h28byrecognizingitasthevalueofacertainderivative51markEvaluatelimhh083A8Beln2CD0E8ln2ln2fxhfxandsowhenxaSolutionWeknowthatbythedenitionofderivativefxlimh0hfahfawehavefalimForthegivenlimitwehaveh0h3h3h32822limlimh0h0hh
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