Active Calculus - Gvsu - Grand Valley State University

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6 1.2. THE NOTION OF LIMITActivity 1.4.Estimate the value of each of the following limits by constructing appropriate tables of values.Then determine the exact value of the limit by using algebra to simplify the function. Finally,plot each function on an appropriate interval to check your result visually.(a) limx→1x 2 − 1x − 1(b) limx→0(2 + x) 3 − 8x(c) limx→0√ x + 1 − 1x⊳
1.2. THE NOTION OF LIMIT 7Activity 1.5.Consider a moving object whose position function is given by s(t) = t 2 , where s is measuredin meters and t is measured in minutes.(a) Determine a simplified expression for the average velocity of the object on the interval[3, 3 + h].(b) Determine the average velocity of the object on the interval [3, 3.2]. Include units onyour answer.(c) Determine the instantaneous velocity of the object when t = 3. Include units on youranswer.⊳
Page 1: Active CalculusMatt Boelkins, Lead
Page 5 and 6: Chapter 1Understanding the Derivati
Page 7 and 8: 1.1. HOW DO WE MEASURE VELOCITY? 3A
Page 9: 1.2. THE NOTION OF LIMIT 51.2 The n
Page 13 and 14: 1.3. THE DERIVATIVE OF A FUNCTION A
Page 15 and 16: 1.3. THE DERIVATIVE OF A FUNCTION A
Page 17 and 18: 1.4. THE DERIVATIVE FUNCTION 131.4
Page 19 and 20: 1.4. THE DERIVATIVE FUNCTION 15rsxx
Page 21 and 22: 1.5. INTERPRETING THE DERIVATIVE AN
Page 23 and 24: 1.5. INTERPRETING THE DERIVATIVE AN
Page 25 and 26: 1.6. THE SECOND DERIVATIVE 21(a) In
Page 27 and 28: 1.6. THE SECOND DERIVATIVE 23• on
Page 29 and 30: 1.6. THE SECOND DERIVATIVE 25ffxxf
Page 31 and 32: 1.7. LIMITS, CONTINUITY, AND DIFFER
Page 33 and 34: 1.7. LIMITS, CONTINUITY, AND DIFFER
Page 35 and 36: 1.8. THE TANGENT LINE APPROXIMATION
Page 37 and 38: Chapter 2Computing Derivatives2.1 E
Page 39 and 40: 2.1. ELEMENTARY DERIVATIVE RULES 35
Page 41 and 42: 2.2. THE SINE AND COSINE FUNCTIONS
Page 43 and 44: 2.2. THE SINE AND COSINE FUNCTIONS
Page 45 and 46: 2.3. THE PRODUCT AND QUOTIENT RULES
Page 47 and 48: 2.3. THE PRODUCT AND QUOTIENT RULES
Page 49 and 50: 2.4. DERIVATIVES OF OTHER TRIGONOME
Page 51 and 52: 2.4. DERIVATIVES OF OTHER TRIGONOME
Page 53 and 54: 2.5. THE CHAIN RULE 492.5 The chain
Page 55 and 56: 2.5. THE CHAIN RULE 51Activity 2.14
Page 57 and 58: 2.6. DERIVATIVES OF INVERSE FUNCTIO
Page 59 and 60: 2.6. DERIVATIVES OF INVERSE FUNCTIO
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2.7. DERIVATIVES OF FUNCTIONS GIVEN
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2.7. DERIVATIVES OF FUNCTIONS GIVEN
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2.8. USING DERIVATIVES TO EVALUATE
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2.8. USING DERIVATIVES TO EVALUATE
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Chapter 3Using Derivatives3.1 Using
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3.1. USING DERIVATIVES TO IDENTIFY
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3.1. USING DERIVATIVES TO IDENTIFY
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3.2. USING DERIVATIVES TO DESCRIBE
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3.2. USING DERIVATIVES TO DESCRIBE
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3.3. GLOBAL OPTIMIZATION 75Activity
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3.3. GLOBAL OPTIMIZATION 77Activity
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3.4. APPLIED OPTIMIZATION 79Activit
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3.4. APPLIED OPTIMIZATION 81Activit
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3.5. RELATED RATES 833.5 Related Ra
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3.5. RELATED RATES 85Activity 3.15.
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3.5. RELATED RATES 87Activity 3.17.
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Chapter 4The Definite Integral4.1 D
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4.1. DETERMINING DISTANCE TRAVELED
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4.1. DETERMINING DISTANCE TRAVELED
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4.2. RIEMANN SUMS 95⊲⊳
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4.2. RIEMANN SUMS 97Activity 4.5.Su
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4.3. THE DEFINITE INTEGRAL 994.3 Th
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4.3. THE DEFINITE INTEGRAL 101Activ
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4.3. THE DEFINITE INTEGRAL 103Activ
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4.4. THE FUNDAMENTAL THEOREM OF CAL
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4.4. THE FUNDAMENTAL THEOREM OF CAL
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Active Calculus - Gvsu - Grand Valley State University

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