Active Calculus - Gvsu - Grand Valley State University

More documents

Recommendations

Info

86 3.5. RELATED RATESActivity 3.16.As pictured in the applet at http://gvsu.edu/s/9q, a skateboarder who is 6 feet tall ridesunder a 15 foot tall lamppost at a constant rate of 3 feet per second. We are interested inunderstanding how fast his shadow is changing at various points in time.(a) Draw an appropriate right triangle that represents a snapshot in time of the skateboarder,lamppost, and his shadow. Let x denote the horizontal distance from the baseof the lamppost to the skateboarder and s represent the length of his shadow. Labelthese quantities, as well as the skateboarder’s height and the lamppost’s height on thediagram.(b) Observe that the skateboarder and the lamppost represent parallel line segments in thediagram, and thus similar triangles are present. Use similar triangles to establish anequation that relates x and s.(c) Use your work in (b) to find an equation that relates dxdtanddsdt .(d) At what rate is the length of the skateboarder’s shadow increasing at the instant theskateboarder is 8 feet from the lamppost?(e) As the skateboarder’s distance from the lamppost increases, is his shadow’s length increasingat an increasing rate, increasing at a decreasing rate, or increasing at a constantrate?(f) Which is moving more rapidly: the skateboarder or the tip of his shadow? Explain, andjustify your answer.⊳
3.5. RELATED RATES 87Activity 3.17.A baseball diamond is 90 ′ square. A batter hits a ball along the third base line runs to first base.At what rate is the distance between the ball and first base changing when the ball is halfwayto third base, if at that instant the ball is traveling 100 feet/sec? At what rate is the distancebetween the ball and the runner changing at the same instant, if at the same instant the runneris 1/8 of the way to first base running at 30 feet/sec?⊳
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 and 10:
1.2. THE NOTION OF LIMIT 51.2 The n
Page 11 and 12:
1.2. THE NOTION OF LIMIT 7Activity
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
Page 61 and 62: 2.7. DERIVATIVES OF FUNCTIONS GIVEN
Page 63 and 64: 2.7. DERIVATIVES OF FUNCTIONS GIVEN
Page 65 and 66: 2.8. USING DERIVATIVES TO EVALUATE
Page 67 and 68: 2.8. USING DERIVATIVES TO EVALUATE
Page 69 and 70: Chapter 3Using Derivatives3.1 Using
Page 71 and 72: 3.1. USING DERIVATIVES TO IDENTIFY
Page 73 and 74: 3.1. USING DERIVATIVES TO IDENTIFY
Page 75 and 76: 3.2. USING DERIVATIVES TO DESCRIBE
Page 77 and 78: 3.2. USING DERIVATIVES TO DESCRIBE
Page 79 and 80: 3.3. GLOBAL OPTIMIZATION 75Activity
Page 81 and 82: 3.3. GLOBAL OPTIMIZATION 77Activity
Page 83 and 84: 3.4. APPLIED OPTIMIZATION 79Activit
Page 85 and 86: 3.4. APPLIED OPTIMIZATION 81Activit
Page 87 and 88: 3.5. RELATED RATES 833.5 Related Ra
Page 89: 3.5. RELATED RATES 85Activity 3.15.
Page 93 and 94: Chapter 4The Definite Integral4.1 D
Page 95 and 96: 4.1. DETERMINING DISTANCE TRAVELED
Page 97 and 98: 4.1. DETERMINING DISTANCE TRAVELED
Page 99 and 100: 4.2. RIEMANN SUMS 95⊲⊳
Page 101 and 102: 4.2. RIEMANN SUMS 97Activity 4.5.Su
Page 103 and 104: 4.3. THE DEFINITE INTEGRAL 994.3 Th
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
show all

Active Calculus - Gvsu - Grand Valley State University

Create successful ePaper yourself

Delete template?

Save as template?