Calculus 2nd Edition Rogawski

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70 CHAPTER 2 LIMITS 50. Sawtooth Function Draw the graph of f (x) = x − [x]. At which points is f discontinuous? Is it left- or right-continuous at those points? In Exercises 51–54, sketch the graph of f (x). At each point of discontinuity, state whether f is left- or right-continuous. { x 2 for x ≤ 1 51. f (x) = 2 − x for x>1 ⎧ ⎨x + 1 for x
SECTION 2.5 Evaluating Limits Algebraically 71 84. Which of the following quantities would be represented by continuous functions of time and which would have one or more discontinuities? (a) Velocity of an airplane during a flight (b) Temperature in a room under ordinary conditions (c) Value of a bank account with interest paid yearly (d) The salary of a teacher (e) The population of the world 85. In 2009, the federal income tax T (x) on income of x dollars (up to $82,250) was determined by the formula ⎧ ⎪⎨ 0.10x for 0 ≤ x
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Publisher: Ruth Baruth Senior Acqui
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To Julie
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CONTENTS CALCULUS Chapter 1 PRECALC
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ABOUT JON ROGAWSKI As a successful
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x PREFACE Placement of Taylor Polyn
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xii PREFACE MEDIA Online Homework O
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xiv PREFACE FEATURES Conceptual Ins
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xvi PREFACE ACKNOWLEDGMENTS Jon Rog
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xviii PREFACE Seminole Community Co
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xx PREFACE University; Legunchim L.
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xxii PREFACE It is a pleasant task
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2 CHAPTER 1 PRECALCULUS REVIEW |a|
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4 CHAPTER 1 PRECALCULUS REVIEW y y
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6 CHAPTER 1 PRECALCULUS REVIEW Antl
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8 CHAPTER 1 PRECALCULUS REVIEW Two
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10 CHAPTER 1 PRECALCULUS REVIEW •
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12 CHAPTER 1 PRECALCULUS REVIEW 61.
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14 CHAPTER 1 PRECALCULUS REVIEW The
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16 CHAPTER 1 PRECALCULUS REVIEW Sol
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18 CHAPTER 1 PRECALCULUS REVIEW The
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Page 76 and 77: 50 CHAPTER 2 LIMITS The limit conce
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Page 98 and 99: 72 CHAPTER 2 LIMITS Other indetermi
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Page 112 and 113: 86 CHAPTER 2 LIMITS Exercises 1. Wh
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Page 116 and 117: 90 CHAPTER 2 LIMITS (a) f (c) = 3 h
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Page 120 and 121: 94 CHAPTER 2 LIMITS Because we are
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Page 124 and 125: 98 CHAPTER 2 LIMITS Further Insight
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Page 128 and 129: 102 CHAPTER 3 DIFFERENTIATION y y y
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120 CHAPTER 3 DIFFERENTIATION 62. S
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122 CHAPTER 3 DIFFERENTIATION REMIN
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124 CHAPTER 3 DIFFERENTIATION REMIN
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126 CHAPTER 3 DIFFERENTIATION 3.3 E
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128 CHAPTER 3 DIFFERENTIATION Furth
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130 CHAPTER 3 DIFFERENTIATION (b) T
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132 CHAPTER 3 DIFFERENTIATION • S
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134 CHAPTER 3 DIFFERENTIATION FIGUR
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136 CHAPTER 3 DIFFERENTIATION 20. T
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138 CHAPTER 3 DIFFERENTIATION F(r)
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140 CHAPTER 3 DIFFERENTIATION EXAMP
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142 CHAPTER 3 DIFFERENTIATION Exerc
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144 CHAPTER 3 DIFFERENTIATION CAUTI
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146 CHAPTER 3 DIFFERENTIATION π
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148 CHAPTER 3 DIFFERENTIATION (c) B
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150 CHAPTER 3 DIFFERENTIATION Chris
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152 CHAPTER 3 DIFFERENTIATION EXAMP
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156 CHAPTER 3 DIFFERENTIATION 4 3 2
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158 CHAPTER 3 DIFFERENTIATION Notic
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160 CHAPTER 3 DIFFERENTIATION We co
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162 CHAPTER 3 DIFFERENTIATION y y 2
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164 CHAPTER 3 DIFFERENTIATION Both
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166 CHAPTER 3 DIFFERENTIATION Step
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170 CHAPTER 3 DIFFERENTIATION Exerc
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172 CHAPTER 3 DIFFERENTIATION y (I)
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174 CHAPTER 3 DIFFERENTIATION 85. A
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176 CHAPTER 4 APPLICATIONS OF THE D
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5 THE INTEGRAL The basic problem in
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246 CHAPTER 5 THE INTEGRAL f (a + 2
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248 CHAPTER 5 THE INTEGRAL Linearit
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250 CHAPTER 5 THE INTEGRAL Computin
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252 CHAPTER 5 THE INTEGRAL 30 20 10
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254 CHAPTER 5 THE INTEGRAL • If f
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256 CHAPTER 5 THE INTEGRAL In Exerc
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258 CHAPTER 5 THE INTEGRAL c 1 c 2
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260 CHAPTER 5 THE INTEGRAL y f(c i
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262 CHAPTER 5 THE INTEGRAL y y = x
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264 CHAPTER 5 THE INTEGRAL • The
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266 CHAPTER 5 THE INTEGRAL 31. ∫
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268 CHAPTER 5 THE INTEGRAL Proof Th
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270 CHAPTER 5 THE INTEGRAL We know
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272 CHAPTER 5 THE INTEGRAL ∫ b
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274 CHAPTER 5 THE INTEGRAL Proof Fi
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276 CHAPTER 5 THE INTEGRAL y y = f(
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278 CHAPTER 5 THE INTEGRAL 2 1 0
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280 CHAPTER 5 THE INTEGRAL EXAMPLE
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282 CHAPTER 5 THE INTEGRAL In Secti
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284 CHAPTER 5 THE INTEGRAL 20. To m
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286 CHAPTER 5 THE INTEGRAL In gener
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288 CHAPTER 5 THE INTEGRAL ∫ EXAM
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290 CHAPTER 5 THE INTEGRAL 5.6 SUMM
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292 CHAPTER 5 THE INTEGRAL ∫ π/2
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294 CHAPTER 5 THE INTEGRAL ∫ 5 35
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6 APPLICATIONS OF THE INTEGRAL In t
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298 CHAPTER 6 APPLICATIONS OF THE I
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340 CHAPTER 7 EXPONENTIAL FUNCTIONS
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414 CHAPTER 8 TECHNIQUES OF INTEGRA
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9 FURTHER APPLICATIONS OF THE INTEG
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480 CHAPTER 9 FURTHER APPLICATIONS
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514 C H A P T E R 10 INTRODUCTION T
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544 C H A P T E R 11 INFINITE SERIE
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614 C H A P T E R 12 PARAMETRIC EQU
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664 C H A P T E R 13 VECTOR GEOMETR
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( x 5 ) 2 + ( y 7 ) 2 + ( z 9 712 C
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( x a 714 C H A P T E R 13 VECTOR G
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730 C H A P T E R 14 CALCULUS OF VE
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15 DIFFERENTIATION IN SEVERAL VARIA
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782 C H A P T E R 15 DIFFERENTIATIO
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16 MULTIPLE INTEGRATION Integrals o
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868 C H A P T E R 16 MULTIPLE INTEG
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946 C H A P T E R 17 LINE AND SURFA
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1000 C H A P T E R 17 LINE AND SURF
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1010 C H A P T E R 18 FUNDAMENTAL T
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A2 APPENDIX A THE LANGUAGE OF MATHE
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B PROPERTIES OF REAL NUMBERS “The
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A10 APPENDIX B PROPERTIES OF REAL N
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A12 APPENDIX B PROPERTIES OF REAL N
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A14 APPENDIX C INDUCTION AND THE BI
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A16 APPENDIX C INDUCTION AND THE BI
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D ADDITIONAL PROOFS In this appendi
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A20 APPENDIX D ADDITIONAL PROOFS TH
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A22 APPENDIX D ADDITIONAL PROOFS Th
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A28 ANSWERS TO ODD-NUMBERED EXERCIS
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A120 REFERENCES Chapter 3 Review (E
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A122 REFERENCES Section 15.8 (EX 42
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A124 PHOTO CREDITS PAGE 410 left Li
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I2 INDEX asymptotic behavior, 81, 2
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I4 INDEX curvilinear coordinates, 9
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I6 INDEX Fourier Series, 422 fracti
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I8 INDEX integrands, 235, 259 and i
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I10 INDEX monotonic functions, 249
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I12 INDEX rate of change (ROC), 14,
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I14 INDEX temperature: directional
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Calculus 2nd Edition Rogawski

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