Active Calculus - Gvsu - Grand Valley State University

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64 2.8. USING DERIVATIVES TO EVALUATE LIMITSActivity 2.24.Evaluate each of the following limits. If you use L’Hopital’s Rule, indicate where it was used,and be certain its hypotheses are met before you apply it.x(a) limx→∞ ln(x)(b)(c)(d)limx→∞e x + x2e x + x 2ln(x)limx→0 + 1xtan(x)limx→ π − x − π 2 2(e)limx→∞ xe−x⊳
Chapter 3Using Derivatives3.1 Using derivatives to identify extreme values of a functionPreview Activity 3.1. Consider the function h given by the graph in Figure 3.1. Use the graph toanswer each of the following questions.2y = h(x)1-2 -1 1 2-1-2Figure 3.1: The graph of a function h on the interval [−3, 3].(a) Identify all of the values of c for which h(c) is a local maximum of h.(b) Identify all of the values of c for which h(c) is a local minimum of h.(c) Does h have a global maximum? If so, what is the value of this global maximum?(d) Does h have a global minimum? If so, what is its value?(e) Identify all values of c for which h ′ (c) = 0.65
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Active CalculusMatt Boelkins, Lead
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Chapter 1Understanding the Derivati
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1.1. HOW DO WE MEASURE VELOCITY? 3A
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1.2. THE NOTION OF LIMIT 51.2 The n
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1.2. THE NOTION OF LIMIT 7Activity
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1.3. THE DERIVATIVE OF A FUNCTION A
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1.3. THE DERIVATIVE OF A FUNCTION A
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Page 31 and 32: 1.7. LIMITS, CONTINUITY, AND DIFFER
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Page 35 and 36: 1.8. THE TANGENT LINE APPROXIMATION
Page 37 and 38: Chapter 2Computing Derivatives2.1 E
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Page 41 and 42: 2.2. THE SINE AND COSINE FUNCTIONS
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Page 45 and 46: 2.3. THE PRODUCT AND QUOTIENT RULES
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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
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Page 79 and 80: 3.3. GLOBAL OPTIMIZATION 75Activity
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Page 83 and 84: 3.4. APPLIED OPTIMIZATION 79Activit
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Page 105 and 106: 4.3. THE DEFINITE INTEGRAL 101Activ
Page 107 and 108: 4.3. THE DEFINITE INTEGRAL 103Activ
Page 109 and 110: 4.4. THE FUNDAMENTAL THEOREM OF CAL
Page 111: 4.4. THE FUNDAMENTAL THEOREM OF CAL
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Active Calculus - Gvsu - Grand Valley State University

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