Explanation Given information: The date on the temperature(T) at a location on the moon t minutes into an eclipse. Approximate the derivative with the symmetric difference quotient (SDQ) approximation T ′ ( t ) ≈ T ( t + 20 ) − T ( t − 20 ) 40 Calculation: Now, check the rate of temperature on all value of t. for t = 20 T ′ ( 0 ) = T ( 20 + 20 ) − T ( 20 − 20 ) 40 = T ( 40 ) − T ( 0 ) 40 = 7 − 45 40 = − 0.95 for t = 40 T ′ ( 40 ) = T ( 60 ) − T ( 20 ) 40 = − 33 − 37 40 = − 1.75 f o r t = 60 T ′ ( 60 ) = T ( 80 ) − T ( 40 ) 40 = − 61 − 7 40 = − 1.7 f o r t = 80 T ′ ( 80 ) = T ( 100 ) − T ( 60 ) 40 = − 78 + 33 40 = − 1.125 f o r t = 100 T ′ ( 100 ) = T ( 120 ) − T ( 80 ) 40 = − 86 + 61 40 = − 0.625 f o r t = 120 T ′ ( 120 ) = T ( 140 ) − T ( 100 ) 40 = − 91 + 78 40 = − 0.325 f o r t = 140 T ′ ( 140 ) = T ( 160 ) − T ( 120 ) 40 = − 95 + 86 40 = − 0 To determine (b) The value of t which give the fastest rate of decrease temperature and the rate of change. t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 T 45 37 7 − 33 − 61 − 78 − 86 − 91 − 95 − 97 − 99 − 101 − 84 − 33 12 37

4th Edition

ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 3.4, Problem 12E

To determine

(a)

The value of t which give the fastest rate of increase temperature and the rate of change.

t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37

To determine

(b)

The value of t which give the fastest rate of decrease temperature and the rate of change.

t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37

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Chapter 3.4, Problem 11E

Chapter 3.4, Problem 13E

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Chapter 3 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 6PQ Ch. 3.1 - Prob. 7PQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E

Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - 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(a) The value of t which give the fastest rate of increase temperature and the rate of change. t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 T 45 37 7 − 33 − 61 − 78 − 86 − 91 − 95 − 97 − 99 − 101 − 84 − 33 12 37

Solution Summary: The author explains the SDQ approximation of the temperature at a location on the moon t minutes into an eclipse.

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(a)

The value of t which give the fastest rate of increase temperature and the rate of change.

t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37

(b)

The value of t which give the fastest rate of decrease temperature and the rate of change.

t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37

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Chapter 3 Solutions

t	0	20	40	60	80	100	120	140	160	180	200	220	240	260	280	300
T	45	37	7	−33	−61	−78	−86	−91	−95	−97	−99	−101	−84	−33	12	37

(a) The value of t which give the fastest rate of increase temperature and the rate of change. t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 T 45 37 7 − 33 − 61 − 78 − 86 − 91 − 95 − 97 − 99 − 101 − 84 − 33 12 37

Solution Summary: The author explains the SDQ approximation of the temperature at a location on the moon t minutes into an eclipse.

Videos

(a) The value of t which give the fastest rate of increase temperature and the rate of change. t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37

(b) The value of t which give the fastest rate of decrease temperature and the rate of change. t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37

Want to see the full answer?

Chapter 3 Solutions

(a)

The value of t which give the fastest rate of increase temperature and the rate of change.

t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37

(b)

The value of t which give the fastest rate of decrease temperature and the rate of change.

t 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

T 45 37 7 −33 −61 −78 −86 −91 −95 −97 −99 −101 −84 −33 12 37