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Math137+138 Solution.pdf

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Department
Mathematics
Course
MATH 137
Professor
Richard Ennis
Semester
Fall

Description
CONTENTSIntroduction1Chapter1Functions2Chapter2LimitsandContinuity43Chapter3TheDerivative65Chapter4LogarithmicandExponentialFunctions99Chapter5AnalysisofFunctionsandTheirGraphs139Chapter6ApplicationsoftheDerivative177Chapter7Integration209Chapter8ApplicationsoftheDeniteIntegralinGeometryScienceandEngineering256Chapter9PrinciplesofIntegralEvaluation292Chapter10MathematicalModelingwithDifferentialEquations343Chapter11InniteSeries361Chapter12AnalyticGeometryinCalculus408Chapter13ThreeDimensionalSpaceVectors448Chapter14VectorValuedFunctions490Chapter15PartialDerivatives524Chapter16MultipleIntegrals573Chapter17TopicsinVectorCalculus608AppendixARealNumbersIntervalsandInequalities640AppendixBAbsoluteValue647AppendixCCoordinatePlanesandLines650AppendixDDistanceCirclesandQuadraticEquations658AppendixETrigonometryReview668AppendixFSolvingPolynomialEquations674CALCULUSANewHorizonfromAncientRootsEXERCISESETFORINTRODUCTION411231ax01231231231000x123123123123123x999x123x999333115bx12777710x1277777so9x10xx115x9cx3807818181100x380781818199x3769743769744188620943376974x99990011005505374296d0429600004296100001250repeatsz2214285732aisirrationalandthushasanonrepeatingdecimalexpansionwhereas722b7pp3336322632233555517151715ppb3a711062511372571557155p5171563333pdc106257155221625682TheareaofacircleofradiusrisDrr4aIfristheradiusthenD2rso99812so25681wastheapproximationusedforrb25681316049227314268and314159so25681isworsethan2275Therstseriestakentotentermsaddsto30418thesecondasprintedaddsto3141611111116a0111111910100100010000100000100000018518520185185b27101001000100001000001000000311111140311111c45101001000100001000001000000636363706363637a1110100100010000100000100000024242480242424b3310100100010000100000100000041666650416666c121010010001000010000010000008a1217517321b132332238223619a1428752654926458b12551378697227072670711111abxaxxaxetcThenbxxxxa10aLetx1213212n1n222soallthexsaredistinctthereareinnitelymanyofthemandtheyallliebetweenaandbibx09999910x9999999x9x1c1999999209999991yesitisconsistentasallthreeareequald10x9xsox991Theyareequal1CHAPTER1FunctionsEXERCISESET111aaround1943b19604200cnoyouneedtheyearspopulationdwarmarketingtechniquesenewsofhealthrisksocialpressureantismokingcampaignsincreasedtaxation2a198935600b198332000cthersttwoyearsthecurveissteeperdownhill3a292023529bnonecy028atx26y22atx12d175x215eymaxmin4ax14bnonecy19atx6y2atx0dx035eymaxmin1nomaximumvalue5ax24bnonecx24xdymin1nomaximumvalue6ax9bnonecx25dymin7aBreakscouldbecausedbywarpestilenceoodearthquakesforexamplebCdecreasesforeighthourstakesajumpupwardsandthenrepeats8aYesifthethermometerisnotnearawindowordoororothersourceofsuddentemperaturechangebThenumberisalwaysanintegersothechangesareinmovementsjumpsofatleastoneunit9aIfthesideadjacenttothebuildinghaslengthxthenLx2ySinceAxy1000Lx2000xbx0andxmustbesmallerthanthewidthofthebuildingwhichwasnotgivendL8944c120min20808010aVlwh62x62xxbFromthegureitisclearthat0x3dV16c20max0302
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