Schaum's Outline of Theory and Problems of Beginning Calculus

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Chapter 37Inverse Trigonometric Functions29237.1 One-One Functions 29237.2 Inverses of Restricted Trigonometric Functions 293Chapter 38Integration by PartsChapter 39Trigonometric Integrands and Trigonometric Substitutions30531139.1 Integration of Trigonometric Functions 31139.2 Trigonometric Substitutions 313Chapter 40Integration of Rational Functions; The Method of Partial FractionsAppendix ATrigonometric FormulasAppendix BBasic Integration FormulasAppendix CGeometric Formulas320329330331Appendix DTrigonometric FunctionsAppendix ENatural LogarithmsAppendix FExponential Functions332333334Answers to Supplementary Problem 335Index 371
Page 4: To the memory of my father, Joseph,
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Page 12: 6.2 Symmetry about a Point 42Chapte
Page 16: Chapter 18Rectilinear Motion and In
Page 20: Chapter 32Applications of Integrati
Page 26: Chapter 1Coordinate Systems on a Li
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Page 40: Chapter 2Coordinate Systems in a Pl
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Page 52: Chapter 3Graphs of EquationsConside
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Chapter 4Straight Lines4.1 SLOPEIf
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26 STRAIGHT LINES [CHAP. 4f’Fig.
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28 STRAIGHT LINES [CHAP. 4Therefore
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30 STRAIGHT LINES [CHAP. 4Solve the
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32 STRAIGHT LINES [CHAP. 4Fig. 4-12
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34 STRAIGHT LINES [CHAP. 44.144.154
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Chapter 5Intersections of GraphsThe
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38INTERSECTIONS OF GRAPHS [CHAP. 5S
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40 INTERSECTIONS OF GRAPHS [CHAP. 5
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42 SYMMETRY[CHAP. 6Consider the gra
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44 SYMMETRY [CHAP. 6(c) The line is
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Chapter 7Functions and Their Graphs
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48 FUNCTIONS AND THEIR GRAPHS[CHAP.
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50 FUNCTIONS AND THEIR GRAPHS [CHAP
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54FUNCTIONS AND THEIR GRAPHS [CHAP.
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60 LIMITS [CHAP. 8PROPERTY 111.EXAM
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h,62 LIMITS [CHAP. 8Notice that the
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64 LIMITS[CHAP. 8tYII-t------IIII-I
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66LIMITS [CHAP. 88.10 (a)(b)x4 - 1F
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68 SPECIAL LIMITS [CHAP. 99.2 INFIN
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70 SPECIAL LIMITS [CHAP. 9x-2EXAMPL
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72 SPECIAL LIMITS [CHAP. 9EXAMPLE A
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74 SPECIAL LIMITS [CHAP. 9GENERAL R
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and76 SPECIAL LIMITS [CHAP. 9Supple
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Chapter 1010.1 DEFIMON AND PROPERTI
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80 CONTINUITY [CHAP. 10(b) The func
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82IYCONTINUITYI’[CHAP. 100I X 0 1
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84CONTINUITY[CHAP. 10YY0T'-3 -2 -1
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Chapter 11The Slope of a Tangent Li
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88 THE SLOPE OF A TANGENT LINE [CHA
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90 THE SLOPE OF A TANGENT LINE [CHA
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Chapter 12The expression for the sl
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TTHE DERIVATIVE [CHAP. 12EXAMPLESD,
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96 THE DERIVATIVE [CHAP. 12(b) Forf
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h,h,98 THE DERIVATIVE [CHAP. 12(b)
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100 MORE ON THE DERIVATIVE [CHAP. 1
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102 MORE ON THE DERIVATIVE [CHAP. 1
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Chapter 14Maximum and Minimum Probl
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106 MAXIMUM AND MINIMUM PROBLEMS [C
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0*1114 MAXIMUM AND MINIMUM PROBLEMS
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Chapter 15The Chain RulelS.lCOMPOSI
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118 THE CHAIN RULE [CHAP. 15EXAMPLE
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4)1)120 THE CHAIN RULE [CHAP. 15The
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122 THE CHAIN RULE [CHAP. 15The onl
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124 THE CHAIN RULE [CHAP. 1515.15 F
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Chapter 16Implicit DifferentiationA
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128 IMPLICIT DIFFERENTIATION[CHAP.
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130 THE MEAN-VALUE THEOREM AND THE
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Chapter 18Rectilinear Motion and In
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138 RECTILINEAR MOTION AND INSTANTA
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144 INSTANTANEOUS RATE OF CHANGE[CH
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146 INSTANTANEOUS RATE OF CHANGE [C
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148 RELATED RATES [CHAP. 20In Fig.
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150 RELATED RATES [CHAP. 20- XFig.
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152 RELATED RATES[CHAP. 20and, by (
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154 RELATED RATES [CHAP. 2020.21 A
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156 APPROXIMATION BY DIFFERENTIALS;
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158 APPROXIMATION BY DIFFERENTIALS;
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1 60APPROXIMATION BY DIFFERENTIALS;
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1 62 HIGHER-ORDER DERIVATIVES [CHAP
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~~164 HIGHER-ORDER DERIVATIVES [CHA
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166 HIGHER-ORDER DERIVATIVES [CHAP.
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168 THE SECOND DERIVATIVE AND GRAPH
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23.7 If, for all x,f’(x) > 0 andf
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180 MORE MAXIMUM AND MINIMUM PROBLE
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186 ANGLE MEASURE [CHAP. 25and so o
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188 ANGLE MEASURE [CHAP. 25Solved P
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Chapter 2626.1 GENERAL DEFINITIONSi
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192 SINE AND COSINE FUNCTIONS [CHAP
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~~~ ~196 SINE AND COSINE FUNCTIONS
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Chapter 27Graphs and Derivatives of
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204 GRAPHS AND DERIVATIVES OF SINE
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212GRAPHS AND DERIVATIVES OF SINE A
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Chapter 28The Tangent andOther Trig
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216 THE TANGENT AND OTHER TRIGONOME
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222 ANTIDERIVATIVES [CHAP. 29EXAMPL
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224 ANTIDERIVATIVES [CHAP. 29(ii) F
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226 ANTIDERIVATIVES [CHAP. 2929.5 A
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228 ANTIDERIVATIVES [CHAP. 2929.13
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230 THE DEFINITE INTEGRAL [CHAP. 30
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232 THE DEFINITE INTEGRAL [CHAP. 30
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234 THE DEFINlTE INTEGRAL (CHAP.[I)
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’)236 THE DEFINITE INTEGRAL [CHAP
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Chapter 31The Fundamental Theorem o
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240 THE FUNDAMENTAL THEOREM OF CALC
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250 APPLICATlONS OF INTEGRATION I:
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252 APPLICATIONS OF INTEGRATION I:
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258 APPLlCATlONS OF INTEGRATION 11:
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260 APPLICATIONS OF INTEGRATION 11:
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266 APPLICATIONS OF INTEGRATION I1
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Chapter 3434.1 DEFlMTlONWe already
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270 THE NATURAL LOGARITHM [CHAP. 34
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272 THE NATURAL LOGARITHM [CHAP. 34
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(b)27434.14THE NATURAL LOGARITHM11(
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276 EXPONENTIAL FUNCTIONS [CHAP. 35
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278EXPONENTIAL FUNCTIONS[CHAP. 3535
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Chapter 36L’HGpital’s Rule ; Ex
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286 L'HOPITAL'S RULE; EXPONENTIAL G
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288 L'H~PITAL'S RULE; EXPONENTIAL G
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290 L'HQPITAL'S RULE; EXPONENTIAL G
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~~~~~~~~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~Chapter
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294 INVERSE TRIGONOMETRIC FUNCTIONS
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above304 INVERSE TRIGONOMETRIC FUNC
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~ du=dx306 INTEGRATION BY PARTS [CH
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308 INTEGRATION BY PARTS[CHAP. 3838
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3 10INTEGRATION BY PARTS[CHAP. 38Su
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312 TRIGONOMETRIC INTEGRANDS AND TR
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Chapter 40Integration of Rational F
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322 THE METHOD OF PARTIAL FRACTIONS
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Appendix BBasic Integration Formula
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0"1"2"3"4"5"6"7"8"9"10"11"12"13"14"
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Appendix F-X0.000.050.100.150.200.2
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336 ANSWERS. TO SUPPLEMENTARY PROBL
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338ANSWERS TO SUPPLEMENTARY PROBLEM
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340 ANSWERS TO SUPPLEMENTARY PROBLE
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R-v QdA 1d 1
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364+I)ANSWERS TO SUPPLEM ENTARY PRO
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Collinear points, 30Common logarith
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Infinite limits, 68Inflection point
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RRadian, 185Radicals, 118Range, 47R
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Schaum's Outline of Theory and Problems of Beginning Calculus

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