- Page 1 and 2: Applied Calculus Math 215 Karl Hein
- Page 3 and 4: Contents Preface iii 0 A Preview 1
- Page 5 and 6: Preface These notes are written for
- Page 7: need the powerful machine developed
- Page 11 and 12: scrutiny, you detect that the graph
- Page 13 and 14: 0.8 0.6 0.4 0.2 -0.2 R(t) 1 2 3 4 t
- Page 15 and 16: Chapter 1 Some Background Material
- Page 17 and 18: 1.1. LINES 9 In application, we are
- Page 19 and 20: 1.1. LINES 11 Exercise 3. Suppose a
- Page 21 and 22: 1.2. PARABOLAS AND HIGHER DEGREE PO
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- Page 25 and 26: 1.2. PARABOLAS AND HIGHER DEGREE PO
- Page 27 and 28: 1.2. PARABOLAS AND HIGHER DEGREE PO
- Page 29 and 30: 1.3. THE EXPONENTIAL AND LOGARITHM
- Page 31 and 32: 1.3. THE EXPONENTIAL AND LOGARITHM
- Page 33 and 34: 1.3. THE EXPONENTIAL AND LOGARITHM
- Page 35 and 36: 1.3. THE EXPONENTIAL AND LOGARITHM
- Page 37 and 38: 1.3. THE EXPONENTIAL AND LOGARITHM
- Page 39 and 40: 1.4. USE OF GRAPHING UTILITIES 31 E
- Page 41 and 42: 1.4. USE OF GRAPHING UTILITIES 33 a
- Page 43 and 44: Chapter 2 The Derivative The deriva
- Page 45 and 46: straight line. There is still a dif
- Page 47 and 48: 6 4 2 -2 -1 1 2 -2 -4 Figure 2.3: E
- Page 49 and 50: Figure 2.4: The radial line is perp
- Page 51 and 52: 2.1. DEFINITION OF THE DERIVATIVE 4
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- Page 55 and 56: 2.2. DIFFERENTIABILITY AS A LOCAL P
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2.3. DERIVATIVES OF SOME BASIC FUNC
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2.3. DERIVATIVES OF SOME BASIC FUNC
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2.3. DERIVATIVES OF SOME BASIC FUNC
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2.4. SLOPES OF SECANT LINES AND RAT
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2.4. SLOPES OF SECANT LINES AND RAT
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2.5. UPPER AND LOWER PARABOLAS 61 o
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2.5. UPPER AND LOWER PARABOLAS 63 6
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2.5. UPPER AND LOWER PARABOLAS 65 2
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2.5. UPPER AND LOWER PARABOLAS 67 I
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2.6. OTHER NOTATIONS FOR THE DERIVA
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2.7. EXPONENTIAL GROWTH AND DECAY 7
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2.7. EXPONENTIAL GROWTH AND DECAY 7
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2.7. EXPONENTIAL GROWTH AND DECAY 7
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2.8. MORE EXPONENTIAL GROWTH AND DE
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2.8. MORE EXPONENTIAL GROWTH AND DE
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2.9. DIFFERENTIABILITY IMPLIES CONT
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2.10. BEING CLOSE VERSUS LOOKING LI
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2.11. RULES OF DIFFERENTIATION 85 t
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2.11. RULES OF DIFFERENTIATION 87 2
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2.11. RULES OF DIFFERENTIATION 89 E
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2.11. RULES OF DIFFERENTIATION 91 2
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2.11. RULES OF DIFFERENTIATION 93 f
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2.11. RULES OF DIFFERENTIATION 95 I
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2.11. RULES OF DIFFERENTIATION 97 T
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2.11. RULES OF DIFFERENTIATION 99 E
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2.11. RULES OF DIFFERENTIATION 101
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2.11. RULES OF DIFFERENTIATION 103
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2.11. RULES OF DIFFERENTIATION 105
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2.11. RULES OF DIFFERENTIATION 107
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2.11. RULES OF DIFFERENTIATION 109
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2.12. IMPLICIT DIFFERENTIATION 111
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2.12. IMPLICIT DIFFERENTIATION 113
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2.13. RELATED RATES 115 Exercise 80
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2.13. RELATED RATES 117 Exercise 86
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2.14. NUMERICAL METHODS 119 Your ca
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2.14. NUMERICAL METHODS 121 There i
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2.14. NUMERICAL METHODS 123 n xn f(
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2.14. NUMERICAL METHODS 125 Practic
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2.14. NUMERICAL METHODS 127 Solutio
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2.14. NUMERICAL METHODS 129 t y(t)
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2.14. NUMERICAL METHODS 131 stabili
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2.14. NUMERICAL METHODS 133 peratur
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2.15. SUMMARY 135 • Quotient rule
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Chapter 3 Applications of the Deriv
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3.2. CAUCHY’S MEAN VALUE THEOREM
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3.2. CAUCHY’S MEAN VALUE THEOREM
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3.2. CAUCHY’S MEAN VALUE THEOREM
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3.3. THE FIRST DERIVATIVE AND MONOT
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3.3. THE FIRST DERIVATIVE AND MONOT
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3.3. THE FIRST DERIVATIVE AND MONOT
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3.3. THE FIRST DERIVATIVE AND MONOT
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3.3. THE FIRST DERIVATIVE AND MONOT
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3.4. THE SECOND AND HIGHER DERIVATI
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3.5. THE SECOND DERIVATIVE AND CONC
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3.5. THE SECOND DERIVATIVE AND CONC
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3.5. THE SECOND DERIVATIVE AND CONC
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3.5. THE SECOND DERIVATIVE AND CONC
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3.6. LOCAL EXTREMA AND INFLECTION P
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3.7. THE FIRST DERIVATIVE TEST 167
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3.7. THE FIRST DERIVATIVE TEST 169
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3.8. THE SECOND DERIVATIVE TEST 171
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3.9. EXTREMA OF FUNCTIONS 173 and a
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3.9. EXTREMA OF FUNCTIONS 175 200 1
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3.9. EXTREMA OF FUNCTIONS 177 P (25
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3.9. EXTREMA OF FUNCTIONS 179 We le
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3.9. EXTREMA OF FUNCTIONS 181 We de
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3.10. DETECTION OF INFLECTION POINT
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3.10. DETECTION OF INFLECTION POINT
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3.11. OPTIMIZATION PROBLEMS 187 3 2
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3.11. OPTIMIZATION PROBLEMS 189 sha
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3.11. OPTIMIZATION PROBLEMS 191 is
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3.11. OPTIMIZATION PROBLEMS 193 (
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3.11. OPTIMIZATION PROBLEMS 195 or
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3.11. OPTIMIZATION PROBLEMS 197 Exe
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3.12. SKETCHING GRAPHS 199 is conca
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3.12. SKETCHING GRAPHS 201 The valu
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Chapter 4 Integration We will intro
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0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 5 6
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4.1. UPPER AND LOWER SUMS 207 So, i
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4.1. UPPER AND LOWER SUMS 209 1.25
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4.1. UPPER AND LOWER SUMS 211 4 3 2
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4.2. INTEGRABILITY AND AREAS 213 4.
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4.2. INTEGRABILITY AND AREAS 215 Pr
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4.2. INTEGRABILITY AND AREAS 217 th
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4.3. SOME ELEMENTARY OBSERVATIONS 2
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4.3. SOME ELEMENTARY OBSERVATIONS 2
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4.4. INTEGRABLE FUNCTIONS 223 4.4 I
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4.5. ANTI-DERIVATIVES 225 In this e
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4.6. THE FUNDAMENTAL THEOREM OF CAL
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4.6. THE FUNDAMENTAL THEOREM OF CAL
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4.6. THE FUNDAMENTAL THEOREM OF CAL
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4.6. THE FUNDAMENTAL THEOREM OF CAL
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4.7. SUBSTITUTION 235 We explain th
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4.7. SUBSTITUTION 237 Solution: We
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4.7. SUBSTITUTION 239 The first ide
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4.7. SUBSTITUTION 241 u = π/2. (Fo
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4.8. AREAS BETWEEN GRAPHS 243 x-coo
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4.9. NUMERICAL INTEGRATION 245 In a
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4.9. NUMERICAL INTEGRATION 247 In t
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4.9. NUMERICAL INTEGRATION 249 an a
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4.10. APPLICATIONS OF THE INTEGRAL
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4.10. APPLICATIONS OF THE INTEGRAL
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4.11. THE EXPONENTIAL AND LOGARITHM
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4.11. THE EXPONENTIAL AND LOGARITHM
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4.11. THE EXPONENTIAL AND LOGARITHM
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4.11. THE EXPONENTIAL AND LOGARITHM
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Chapter 5 Prerequisites from Precal
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5.1. THE REAL NUMBERS 265 A typical
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5.2. INEQUALITIES AND ABSOLUTE VALU
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5.3. FUNCTIONS, DEFINITION AND NOTA
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5.3. FUNCTIONS, DEFINITION AND NOTA
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5.3. FUNCTIONS, DEFINITION AND NOTA
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5.4. GRAPHING EQUATIONS 275 Example
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5.5. TRIGONOMETRIC FUNCTIONS 277 1
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5.5. TRIGONOMETRIC FUNCTIONS 279 40
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5.5. TRIGONOMETRIC FUNCTIONS 281 op
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5.5. TRIGONOMETRIC FUNCTIONS 283 an
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5.5. TRIGONOMETRIC FUNCTIONS 285 A
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5.6. INVERSE FUNCTIONS 287 Observe
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5.6. INVERSE FUNCTIONS 289 5 4 3 2
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5.6. INVERSE FUNCTIONS 291 Exercise
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5.7. NEW FUNCTIONS FROM OLD ONES 29