Calculus This is the free digital calculus text by David R Guichard and others It was submitted to the Free Digital Textbook Initiative in California and will remain unchanged for at least two years The book is in use at Whitman College and is occasionally updated to correct errors and add new material The latest versions may be found by
Calculus I or needing a refresher in some of the early topics in calculus I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from an Algebra or Trig class or contained in other sections of the
calculus book—it is a book to be read Also, the exercises make unusual demands on students Most exercises are not just variants of examples that have been worked in the text In fact, the text has rather few simple “tem-plate” examples Shifts in Emphasis It will also become apparent to you that the text
Oct 09, 2012 · calculus made easy: being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus by f r s second edition, enlarged macmillan and co , limited st martin’s street, london 1914
The book includes some exercises and examples from Elementary Calculus: integration are largely derived from the corresponding portions of Keisler’s book
The book begins with an example that is familiar to everybody who drives a car It is calculus in action-the driver sees it happening The example is the relation between the speedometer and the odometer One measures the speed (or velocity); the other measures the distance traveled We will write v for the velocity, and f for
The AP Calculus Problem Book Publication history: First edition, 2002 Second edition, 2003 Third edition, 2004 Third edition Revised and Corrected, 2005 Fourth edition, 2006, Edited by Amy Lanchester Fourth edition Revised and Corrected, 2007 Fourth edition, Corrected, 2008 This book was produced directly from the author’s LATEX files
Finally, this book steers a path between the terse theorem-proof listing of bare essentials and the bulky down-to-the-student-level books that try to usurp the role of the instructor by a wordy and chatty style It is hoped that most students can, and will, read the book, but it is also assumed that each
[PDF] La DEMARCHE en GRAPHISME - mediaeduscoleducationfr
[PDF] 2017-2018 Official Academic Calendar - Carnegie Mellon University
[PDF] CALENDRIER 2017 FRANCE http://calendarzoznamsk
[PDF] CALENDARUL ADMITERII ÎN ÎNV #258 #354 #258 MÂNTUL LICEAL DE - ISMB
[PDF] ORDIN privind organizarea #537 i desf #259 #537 urarea admiterii în - ISMB
[PDF] Ordinul MEN nr 4794_31 aug 2017_admitere in inv liceal 2018
[PDF] ORDIN privind aprobarea Calendarului admiterii în înv #259 #539 #259 mântul
[PDF] Calendrier scolaire 2017-2018
[PDF] CALENDARUL examenului de bacalaureat na #355 ional - 2017
[PDF] Academic Calendar Spring 2018 - The University of Texas at Dallas
[PDF] Calendar #537 colar 2017 #8211 2018
[PDF] Calendario 2017 -2018 de 185 -195 días SEP pdf - Secretaría de
[PDF] Calendario escolar 2016-2017 (200 días) - gobmx
[PDF] Calendario escolar 2016-2017 (185 días) - gobmx
[PDF] 2018-2019 Calendario Escolar
The AP Calculus
Problem Book
Chuck Garner, Ph.D.
Dedicated to the students who used previous editions of this book!
BC Class of 2003
Will Andersen
Kenny Baskett
Amanda Dugan
Rochelle Dunlap
Daniel Eisenman
Kylene Farmer
Nathan Garcia
Brandon Jackson
Drew Keenan
Amin Makhani
Patrick McGahee
Rachel Meador
Richard Moss
Trent Phillips
John Powell
Blake Serra
Jon Skypek
David Thompson
AB Class of 2003
Ryan Boyd
R. T. Collins
Holly Ellington
Stephen Gibbons
Aly Mawji
Chris McKnight
Franklin Middlebrooks
Kelly Morrison
Julien Norton
Jurod RussellBC Class of 2004
Anita Amin
Anushka Amin
Rachel Atkinson
Max Bernardy
Lindsey Broadnax
Andy Brunton
Mitch Costley
Caitlin Dingle
Krista Firkus
Justin Gilstrap
Casey Haney
Kendra Heisner
Daniel Hendrix
Candace Hogan
Luke Hotchkiss
Shawn Hyde
Whitney Irwin
Garett McLaurin
C. K. Newman
Matt Robuck
Melissa Sanders
Drew Sheffield
Carsten Singh
Andrea Smith
Frankie Snavely
Elizabeth Thai
Ray Turner
Timothy Van Heest
Josh Williams
Ben Wu
Jodie Wu
Michael Wysolovski
Drew Yaun
AB Class of 2004
Brooke Atkinson
Kevin Dirth
Jaimy Lee
Robert Parr
Garion Reddick
Andre Russell
Megan VillanuevaBC Class of 2005
Jonathan Andersen
James Bascle
Eryn Bernardy
Joesph Bost
William Brawley
Alex Hamilton
Sue Ann Hollowell
Vicky Johnson
Kayla Koch
Amy Lanchester
Dana McKnight
Kathryn Moore
Ryan Moore
Candace Murphy
Hannah Newman
Bre"Ana Paige
Lacy Reynolds
Jacob Schiefer
Kevin Todd
Amanda Wallace
Jonathan Wysolovski
Keeli Zanders
AB Class of 2005
Lacey Avery
Alicia Bellis
Mollie Bogle
Carin Godemann
Shawn Kumar
Joe Madsen
Julie Matthews
Jazmine Reaves
Sarah Singh
Andrew Vanstone
Jawaan Washington
Michael Westbury
Jeremy WilkersonBC Class of 2006
John Barnett
Chelsea Britt
Sam Brotherton
Justin Carlin
Ryan Ceciliani
Nicole Fraute
Carin Godemann
Megan Harris
Zack Higbie
Nayoon Kim
Amy Kovac
Julie Leber
Salman Makhani
Julie Matthews
Chris Meador
Sophia Newton
Chris Randall
Nicole Richardson
Britt Schneider
Michaela Simoes
Jesse Smith
AB Class of 2006
Shail Amin
Lucky Baker
Savannah Barrus
Taylor Boggus
Justin Clemons
Kim Dang
Will Gibson
Latiria Hill
John-Lee Hughey
Michael Hyman
Cassandra Lohmeyer
Chris Long
Jason Long
Joseph Long
Cason Lowe
Cassie Lowury
Victoria Nesmith
Dion Roseberry
Cassie Smith
Aniya WatsonBC Class of 2007
Betsey Avery
Aaron Bullock
Cecily Bullock
Daniel Chen
Raymond Clunie
Jim Creager
Katie Dugan
Mitchell Granade
Allyse Keel
Jacob Kovac
Jan Lauritsen
Ally Long
Chris Long
Nick Macie
Will Martin
Justin McKithen
Ruhy Momin
Steven Rouk
Tyler Sigwald
Lauren Troxler
Ryan Young
AB Class of 2007
Melanie Allen
Briana Brimidge
Michelle Dang
Kyle Davis
Holly Dean
Shaunna Duggan
Chris Elder
Kevin Gorman
Jessie Holmes
Gary McCrear
Faith Middlebrooks
D"Andra Myers
Brandi Paige
Miriam Perfecto
Thomas Polstra
Torri Preston
Heather Quinn
Andrew Smith
Nicole ThomasBC Class of 2008
Layla Bouzoubaa
Kevin Brawley
Ashley Chackalayil
Nate Coursey
Michelle Dang
Kathryn Daniel
Justin Easley
Samantha Girardot
Jessie Holmes
Johnathan Johnson
Kathryn Johnson
Tyler Kelly
Rochelle Lobo
Monica Longoria
April Lovering
Kevin Masters
David McCalley
Gary McCrear
Patti Murphy
Sarah Pace
Bijal Patel
Kunal Patel
Miriam Perfecto
Thomas Polstra
James Rives
Khaliliah Smith
Andrew Stover
Aswad Walker
Ashley Williams
AB Class of 2008
Omair Akhtar
John Collins
Rachel Delevett
Kelsey Hinely
Sarah Kustick
Bianca Manahu
Shonette McCalmon
Ansley Mitcham
Tesia Olgetree
Lauren Powell
Xan Reynolds
Lauren Stewart
Matt Wann
Ryan Young
The AP Calculus
Problem Book
Chuck Garner, Ph.D.
Rockdale Magnet School
for Science and Technology
Fourth Edition,
Revised and Corrected, 2008
The AP Calculus Problem Book
Publication history:
First edition, 2002
Second edition, 2003
Third edition, 2004
Third edition Revised and Corrected, 2005
Fourth edition, 2006, Edited by Amy Lanchester
Fourth edition Revised and Corrected, 2007
Fourth edition, Corrected, 2008
This book was produced directly from the author"s L
ATEX files.
Figures were drawn by the author using the TEXdraw package. TI-Calculator screen-shots produced by a TI-83Plus calculator using a TI-Graph Link. L
ATEX (pronounced "Lay-Tek") is a document typesetting program (not a word processor) that is available free fromwww.miktex.org,
which also includes TEXnicCenter, a free and easy-to-use user-interface.
Contents
1 LIMITS7
1.1 Graphs of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 8
1.2 The Slippery Slope of Lines . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 9
1.3 The Power of Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 10
1.4 Functions Behaving Badly . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 11
1.5 Take It to the Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 12
1.6 One-Sided Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 13
1.7 One-Sided Limits (Again) . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 14
1.8 Limits Determined by Graphs . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 15
1.9 Limits Determined by Tables . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 16
1.10 The Possibilities Are Limitless... . . . . . . . . . . . . . . . .. . . . . . . . . . . 17
1.11 Average Rates of Change: Episode I . . . . . . . . . . . . . . . . . .. . . . . . . 18
1.12 Exponential and Logarithmic Functions . . . . . . . . . . . . .. . . . . . . . . . 18
1.13 Average Rates of Change: Episode II . . . . . . . . . . . . . . . . .. . . . . . . . 19
1.14 Take It To the Limit-One More Time . . . . . . . . . . . . . . . . . . .. . . . . 20
1.15 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 21
1.16 Continuously Considering Continuity . . . . . . . . . . . . . .. . . . . . . . . . . 22
1.17 Have You Reached the Limit? . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 23
1.18 Multiple Choice Questions on Limits . . . . . . . . . . . . . . . .. . . . . . . . . 24
1.19 Sample A.P. Problems on Limits . . . . . . . . . . . . . . . . . . . . .. . . . . . 26
Last Year"s Limits Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 27
2 DERIVATIVES35
2.1 Negative and Fractional Exponents . . . . . . . . . . . . . . . . . .. . . . . . . . 36
2.2 Logically Thinking About Logic . . . . . . . . . . . . . . . . . . . . .. . . . . . . 37
2.3 The Derivative By Definition . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 38
2.4 Going Off on a Tangent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39
2.5 Six Derivative Problems . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 40
2.6 Trigonometry: a Refresher . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 41
1
2The AP CALCULUS PROBLEM BOOK
2.7 Continuity and Differentiability . . . . . . . . . . . . . . . . . . .. . . . . . . . . 42
2.8 The RULES: Power Product Quotient Chain . . . . . . . . . . . . . .. . . . . . 43
2.9 Trigonometric Derivatives . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 44
2.10 Tangents, Normals, and Continuity (Revisited) . . . . . .. . . . . . . . . . . . . 45
2.11 Implicit Differentiation . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 46
2.12 The Return of Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 47
2.13 Meet the Rates (They"re Related) . . . . . . . . . . . . . . . . . . .. . . . . . . 48
2.14 Rates Related to the Previous Page . . . . . . . . . . . . . . . . . .. . . . . . . . 49
2.15 Excitement with Derivatives! . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 50
2.16 Derivatives of Inverses . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 51
2.17 D´eriv´e, Derivado, Ableitung, Derivative . . . . . . . . .. . . . . . . . . . . . . . 52
2.18 Sample A.P. Problems on Derivatives . . . . . . . . . . . . . . . .. . . . . . . . . 54
2.19 Multiple-Choice Problems on Derivatives . . . . . . . . . . .. . . . . . . . . . . . 56
Last Year"s Derivatives Test . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 58
3 APPLICATIONS of DERIVATIVES67
3.1 The Extreme Value Theorem . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 68
3.2 Rolle to the Extreme with the Mean Value Theorem . . . . . . . .. . . . . . . . 69
3.3 The First and Second Derivative Tests . . . . . . . . . . . . . . . .. . . . . . . . 70
3.4 Derivatives and Their Graphs . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 71
3.5 Two Derivative Problems . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 73
3.6 Sketching Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 74
3.7 Problems of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 76
3.8 Maximize or Minimize? . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 78
3.9 More Tangents and Derivatives . . . . . . . . . . . . . . . . . . . . . .. . . . . . 80
3.10 More Excitement with Derivatives! . . . . . . . . . . . . . . . . .. . . . . . . . . 81
3.11 Bodies, Particles, Rockets, Trucks, and Canals . . . . . .. . . . . . . . . . . . . 82
3.12 Even More Excitement with Derivatives! . . . . . . . . . . . . .. . . . . . . . . . 84
3.13 Sample A.P. Problems on Applications of Derivatives . .. . . . . . . . . . . . . . 86
3.14 Multiple-Choice Problems on Applications of Derivatives . . . . . . . . . . . . . . 89
Last Year"s Applications of Derivatives Test . . . . . . . . . . . .. . . . . . . . . . . . 92
4 INTEGRALS101
4.1 The ANTIderivative! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 102
4.2 Derivative Rules Backwards . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 103
4.3 The Method of Substitution . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 104
4.4 Using Geometry for Definite Integrals . . . . . . . . . . . . . . . .. . . . . . . . 105
4.5 Some Riemann Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 106
4.6 The MVT and the FTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.7 The FTC, Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 108
4.8 Definite and Indefinite Integrals . . . . . . . . . . . . . . . . . . . .. . . . . . . . 109
4.9 Integrals Involving Logarithms and Exponentials . . . . .. . . . . . . . . . . . . 110
4.10 It Wouldn"t Be Called the Fundamental Theorem If It Wasn"t Fundamental . . . 111
4.11 Definite and Indefinite Integrals Part 2 . . . . . . . . . . . . . .. . . . . . . . . . 113
4.12 Regarding Riemann Sums . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 114
4.13 Definitely Exciting Definite Integrals! . . . . . . . . . . . . .. . . . . . . . . . . . 116
4.14 How Do I Find the Area Under Thy Curve? Let Me Count the Ways... . . . . . . 117
4.15 Three Integral Problems . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 118
CONTENTS3
4.16 Trapezoid and Simpson . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 119
4.17 Properties of Integrals . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 120
4.18 Sample A.P. Problems on Integrals . . . . . . . . . . . . . . . . . .. . . . . . . . 121
4.19 Multiple Choice Problems on Integrals . . . . . . . . . . . . . .. . . . . . . . . . 124
Last Year"s Integrals Test . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 127
5 APPLICATIONS of INTEGRALS135
5.1 Volumes of Solids with Defined Cross-Sections . . . . . . . . .. . . . . . . . . . . 136
5.2 Turn Up the Volume! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 137
5.3 Volume and Arc Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 138
5.4 Differential Equations, Part One . . . . . . . . . . . . . . . . . . . .. . . . . . . 139
5.5 The Logistic Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 140
5.6 Differential Equations, Part Two . . . . . . . . . . . . . . . . . . . .. . . . . . . 141
5.7 Slope Fields and Euler"s Method . . . . . . . . . . . . . . . . . . . . .. . . . . . 142
5.8 Differential Equations, Part Three . . . . . . . . . . . . . . . . . .. . . . . . . . 143
5.9 Sample A.P. Problems on Applications of Integrals . . . . .. . . . . . . . . . . . 144
5.10 Multiple Choice Problems on Application of Integrals .. . . . . . . . . . . . . . 147
Last Year"s Applications of Integrals Test . . . . . . . . . . . . . .. . . . . . . . . . . 150
6 TECHNIQUES of INTEGRATION159
6.1 A Part, And Yet, Apart... . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 160
6.2 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 161
6.3 Trigonometric Substitution . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 162
6.4 Four Integral Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 163
6.5 L"Hˆopital"s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 164
6.6 Improper Integrals! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 165
6.7 The Art of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 166
6.8 Functions Defined By Integrals . . . . . . . . . . . . . . . . . . . . . .. . . . . . 168
6.9 Sample A.P. Problems on Techniques of Integration . . . . .. . . . . . . . . . . 170
6.10 Sample Multiple-Choice Problems on Techniques of Integration . . . . . . . . . . 173
Last Year"s Techniques of Integration Test . . . . . . . . . . . . . .. . . . . . . . . . . 175
7 SERIES, VECTORS, PARAMETRICS and POLAR 183
7.1 Sequences: Bounded and Unbounded . . . . . . . . . . . . . . . . . . .. . . . . . 184
7.2 It is a Question of Convergence... . . . . . . . . . . . . . . . . . . .. . . . . . . . 185
7.3 Infinite Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 186
7.4 Tests for Convergence and Divergence . . . . . . . . . . . . . . . .. . . . . . . . 187
7.5 More Questions of Convergence... . . . . . . . . . . . . . . . . . . .. . . . . . . . 188
7.6 Power Series! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 189
7.7 Maclaurin Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 190
7.8 Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 191
7.9 Vector Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 192
7.10 Calculus with Vectors and Parametrics . . . . . . . . . . . . . .. . . . . . . . . . 193
7.11 Vector-Valued Functions . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 194
7.12 Motion Problems with Vectors . . . . . . . . . . . . . . . . . . . . . .. . . . . . 195
7.13 Polar Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 196
7.14 Differentiation (Slope) and Integration (Area) in Polar . . . . . . . . . . . . . . . 197
7.15 Sample A.P. Problems on Series, Vectors, Parametrics,and Polar . . . . . . . . . 198
4The AP CALCULUS PROBLEM BOOK
7.16 Sample Multiple-Choice Problems on Series, Vectors, Parametrics, and Polar . . 201
Last Year"s Series, Vectors, Parametrics, and Polar Test . .. . . . . . . . . . . . . . . 203
8 AFTER THE A.P. EXAM211
8.1 Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 212
8.2 Surface Area of a Solid of Revolution . . . . . . . . . . . . . . . . .. . . . . . . . 213
8.3 Linear First Order Differential Equations . . . . . . . . . . . .. . . . . . . . . . 214
8.4 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 215
8.5 Newton"s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 216
9 PRACTICE and REVIEW217
9.1 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .218
quotesdbs_dbs23.pdfusesText_29
Calculus This is the free digital calculus text by David R