The AP Calculus Problem Book

1 The AP CalculusProblem Book Chuck Garner, to the students who used previous editions of this book!BC Class of 2003 Will AndersenKenny BaskettAmanda DuganRochelle DunlapDaniel EisenmanKylene FarmerNathan GarciaBrandon JacksonDrew KeenanAmin MakhaniPatrick McGaheeRachel MeadorRichard MossTrent PhillipsJohn PowellBlake SerraJon SkypekDavid ThompsonAB Class of 2003 Ryan BoydR. T. CollinsHolly EllingtonStephen GibbonsAly MawjiChris McKnightFranklin MiddlebrooksKelly MorrisonJulien NortonJurod RussellBC Class of 2004 Anita AminAnushka AminRachel AtkinsonMax BernardyLindsey BroadnaxAndy BruntonMitch CostleyCaitlin DingleKrista FirkusJustin GilstrapCasey HaneyKendra HeisnerDaniel HendrixCandace HoganLuke HotchkissShawn HydeWhitney IrwinGarett McLaurinC. K. NewmanMatt RobuckMelissa SandersDrew SheffieldCarsten SinghAndrea SmithFrankie SnavelyElizabeth ThaiRay TurnerTimothy Van HeestJosh WilliamsBen WuJodie WuMichael WysolovskiDrew YaunAB Class of 2004 Brooke AtkinsonKevin DirthJaimy LeeRobert ParrGarion ReddickAndre RussellMegan VillanuevaBC Class of 2005 Jonathan AndersenJames BascleEryn BernardyJoesph BostWilliam BrawleyAlex HamiltonSue Ann HollowellVicky JohnsonKayla KochAmy LanchesterDana McKnightKathryn MooreRyan MooreCandace MurphyHannah NewmanBre Ana PaigeLacy ReynoldsJacob SchieferKevin ToddAmanda WallaceJonathan WysolovskiKeeli ZandersAB Class of 2005 Lacey AveryAlicia BellisMollie BogleCarin GodemannShawn KumarJoe MadsenJulie MatthewsJazmine ReavesSarah SinghAndrew VanstoneJawaan WashingtonMichael WestburyJeremy WilkersonBC Class of

2 2006 John BarnettChelsea BrittSam BrothertonJustin CarlinRyan CecilianiNicole FrauteCarin GodemannMegan HarrisZack HigbieNayoon KimAmy KovacJulie LeberSalman MakhaniJulie MatthewsChris MeadorSophia NewtonChris RandallNicole RichardsonBritt SchneiderMichaela SimoesJesse SmithAB Class of 2006 Shail AminLucky BakerSavannah BarrusTaylor BoggusJustin ClemonsKim DangWill GibsonLatiria HillJohn-Lee HugheyMichael HymanCassandra LohmeyerChris LongJason LongJoseph LongCason LoweCassie LowuryVictoria NesmithDion RoseberryCassie SmithAniya WatsonBC Class of 2007 Betsey AveryAaron BullockCecily BullockDaniel ChenRaymond ClunieJim CreagerKatie DuganMitchell GranadeAllyse KeelJacob KovacJan LauritsenAlly LongChris LongNick MacieWill MartinJustin McKithenRuhy MominSteven RoukTyler SigwaldLauren TroxlerRyan YoungAB Class of 2007 Melanie AllenBriana BrimidgeMichelle DangKyle DavisHolly DeanShaunna DugganChris ElderKevin GormanJessie HolmesGary McCrearFaith MiddlebrooksD Andra MyersBrandi PaigeMiriam PerfectoThomas PolstraTorri PrestonHeather QuinnAndrew SmithNicole ThomasBC Class of 2008 Layla BouzoubaaKevin BrawleyAshley ChackalayilNate CourseyMichelle DangKathryn DanielJustin EasleySamantha GirardotJessie HolmesJohnathan JohnsonKathryn JohnsonTyler KellyRochelle LoboMonica LongoriaApril LoveringKevin MastersDavid McCalleyGary McCrearPatti MurphySarah PaceBijal PatelKunal PatelMiriam PerfectoThomas PolstraJames RivesKhaliliah SmithAndrew StoverAswad WalkerAshley WilliamsAB Class of 2008 Omair AkhtarJohn CollinsRachel DelevettKelsey HinelySarah KustickBianca ManahuShonette McCalmonAnsley

3 MitchamTesia OlgetreeLauren PowellXan ReynoldsLauren StewartMatt WannRyan YoungThe AP CalculusProblem Book Chuck Garner, Magnet Schoolfor Science and TechnologyFourth Edition,Revised and Corrected, 2008 The AP Calculus Problem BookPublication history:First edition, 2002 Second edition, 2003 Third edition, 2004 Third edition Revised and Corrected, 2005 Fourth edition, 2006, Edited by Amy LanchesterFourth edition Revised and Corrected, 2007 Fourth edition, Corrected, 2008 This book was produced directly from the author s LATEX were drawn by the author using the TEXdraw screen-shots produced by a TI-83 Plus calculator using a TI-Graph (pronounced Lay-Tek ) is a document typesetting program (not a word processor) that is available free ,which also includes TEXnicCenter, a free and easy-to-use Graphs of Functions.

4 The Slippery Slope of Lines .. The Power of Algebra .. Functions Behaving Badly .. Take It to the Limit .. One-Sided Limits .. One-Sided Limits (Again) .. Limits Determined by Graphs .. Limits Determined by Tables .. The Possibilities Are .. Average Rates of Change: Episode I .. Exponential and Logarithmic Functions .. Average Rates of Change: Episode II .. Take It To the Limit One More Time .. Solving Equations .. Continuously Considering Continuity .. Have You Reached the Limit? .. Multiple Choice Questions on Limits .. Sample Problems on Limits .. 26 Last Year s Limits Test .. 272 Negative and Fractional Exponents .. Logically Thinking About Logic .. The Derivative By Definition .. Going Off on a Tangent.

5 Six Derivative Problems .. Trigonometry: a Refresher .. 4112 The AP Calculus Problem Continuity and Differentiability .. The RULES: Power Product Quotient Chain .. Trigonometric Derivatives .. Tangents, Normals, and Continuity (Revisited) .. Implicit Differentiation .. The Return of Geometry .. Meet the Rates (They re Related) .. Rates Related to the Previous Page .. Excitement with Derivatives! .. Derivatives of Inverses .. D eriv e, Derivado, Ableitung, Derivative .. Sample Problems on Derivatives .. Multiple-Choice Problems on Derivatives .. 56 Last Year s Derivatives Test .. 583 APPLICATIONS of The Extreme Value Theorem .. Rolle to the Extreme with the Mean Value Theorem .. The First and Second Derivative Tests .. Derivatives and Their Graphs.

6 Two Derivative Problems .. Sketching Functions .. Problems of Motion .. Maximize or Minimize? .. More Tangents and Derivatives .. More Excitement with Derivatives! .. Bodies, Particles, Rockets, Trucks, and Canals .. Even More Excitement with Derivatives! .. Sample Problems on Applications of Derivatives .. Multiple-Choice Problems on Applications of Derivatives .. 89 Last Year s Applications of Derivatives Test .. 924 The ANTI derivative! .. Derivative Rules Backwards .. The Method of Substitution .. Using Geometry for Definite Integrals .. Some Riemann Sums .. The MVT and the FTC .. The FTC, Graphically .. Definite and Indefinite Integrals .. Integrals Involving Logarithms and Exponentials .. It Wouldn t Be Called the Fundamental Theorem If It Wasn t Fundamental.

7 Definite and Indefinite Integrals Part 2 .. Regarding Riemann Sums .. Definitely Exciting Definite Integrals! .. How Do I Find the Area Under Thy Curve? Let Me Count the .. Three Integral Problems .. Trapezoid and Simpson .. Properties of Integrals .. Sample Problems on Integrals .. Multiple Choice Problems on Integrals .. 124 Last Year s Integrals Test .. 1275 APPLICATIONS of Volumes of Solids with Defined Cross-Sections .. Turn Up the Volume! .. Volume and Arc Length .. Differential Equations, Part One .. The Logistic Curve .. Differential Equations, Part Two .. Slope Fields and Euler s Method .. Differential Equations, Part Three .. Sample Problems on Applications of Integrals .. Multiple Choice Problems on Application of Integrals.

8 147 Last Year s Applications of Integrals Test .. 1506 TECHNIQUES of A Part, And Yet, .. Partial Fractions .. Trigonometric Substitution .. Four Integral Problems .. L H opital s Rule .. Improper Integrals! .. The Art of Integration .. Functions Defined By Integrals .. Sample Problems on Techniques of Integration .. Sample Multiple-Choice Problems on Techniques of Integration .. 173 Last Year s Techniques of Integration Test .. 1757 SERIES, VECTORS, PARAMETRICS and Sequences: Bounded and Unbounded .. It is a Question of .. Infinite Sums .. Tests for Convergence and Divergence .. More Questions of .. Power Series! .. Maclaurin Series .. Taylor Series .. Vector Basics .. Calculus with Vectors and Parametrics .. Vector-Valued Functions.

9 Motion Problems with Vectors .. Polar Basics .. Differentiation (Slope) and Integration (Area) in Polar .. Sample Problems on Series, Vectors, Parametrics,and Polar .. 1984 The AP Calculus Problem Sample Multiple-Choice Problems on Series, Vectors, Parametrics, and Polar .. 201 Last Year s Series, Vectors, Parametrics, and Polar Test .. 2038 AFTER THE Hyperbolic Functions .. Surface Area of a Solid of Revolution .. Linear First Order Differential Equations .. Curvature .. Newton s Method .. 2169 PRACTICE and Algebra .. Derivative Skills .. Can You Stand All These Exciting Derivatives? .. Different Differentiation Problems .. Again! .. Int egrale, Integrale, Integraal, Integral .. Calculus Is an Integral Part of Your Life .. Particles.

10 Areas .. The Deadly Dozen .. Two Volumes and Two Differential Equations .. Differential Equations, Part Four .. More Integrals .. Definite Integrals Requiring Definite Thought .. Just When You Thought Your Problems Were .. Interesting Integral Problems .. Infinitely Interesting Infinite Series .. Getting Serious About Series .. A Series of Series Problems .. 24010 GROUP INVESTIGATIONS241 About the Group Investigations .. Finding the Most Economical Speed for Trucks .. Minimizing the Area Between a Graph and Its Tangent .. The Ice Cream Cone Problem .. Designer Polynomials .. Inventory Management .. Optimal Design of a Steel Drum .. 24611 Calculus LABS247 About the Labs .. 2481: The Intermediate Value Theorem .. 2502: Local Linearity .. 2523: Exponentials.