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2. The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in the following table. Wind speed (km/h) V 20 30 40 1.3 1.5 2.2 2.4 4.9 4.3 6.4 7.7 8.6 5.8 8.9 11.0 12.2 13.8 120 7.4 11.3 14.4 16.6 19.0 60 80 Duration (hours) 5 10 15 20 100 0.6 1.2 1.5 30 0.6 0.6 0.6 0.6 1.5 2.8 4.0 1.5 2.5 2.7 5.2 5.5 40 0.6 1.6 2.8 50 20.5 0.6 2.8 5.8 5.9 9.5 10.1 10.2 14.7 15.3 1.6 21.1 (a) What are the meanings of the partial derivatives dh/av and əh/at? (b) Estimate the values of f(40, 15) and f(40, 15). What are the practical interpretations of these values?

2. The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in the following table. Wind speed (km/h) V 20 30 40 1.3 1.5 2.2 2.4 4.9 4.3 6.4 7.7 8.6 5.8 8.9 11.0 12.2 13.8 120 7.4 11.3 14.4 16.6 19.0 60 80 Duration (hours) 5 10 15 20 100 0.6 1.2 1.5 30 0.6 0.6 0.6 0.6 1.5 2.8 4.0 1.5 2.5 2.7 5.2 5.5 40 0.6 1.6 2.8 50 20.5 0.6 2.8 5.8 5.9 9.5 10.1 10.2 14.7 15.3 1.6 21.1 (a) What are the meanings of the partial derivatives dh/av and əh/at? (b) Estimate the values of f(40, 15) and f(40, 15). What are the practical interpretations of these values?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 50E
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Estimate the value of Duf (30, 20), where u = (i + j)/√2 using the table provided.

2. The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in the following table. Wind speed (km/h) V 20 30 40 60 80 t 100 5 10 15 0.6 1.2 5.8 Duration (hours) 20 0.6 0.6 0.6 1.5 1.5 1.3 1.5 2.2 2.8 4.0 4.3 6.4 2.4 4.9 30 2.5 40 0.6 0.6 1.5 1.6 7.7 8.6 9.5 50 2.7 5.2 5.5 5.8 5.9 10.1 2.8 0.6 1.6 2.8 10.2 8.9 11.0 12.2 13.8 14.7 15.3 120 7.4 11.3 14.4 16.6 19.0 20.5 21.1 (a) What are the meanings of the partial derivatives əh/av and əh/at? (b) Estimate the values of f(40, 15) and fi(40, 15). What are the practical interpretations of these values?
Transcribed Image Text:2. The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in the following table. Wind speed (km/h) V 20 30 40 60 80 t 100 5 10 15 0.6 1.2 5.8 Duration (hours) 20 0.6 0.6 0.6 1.5 1.5 1.3 1.5 2.2 2.8 4.0 4.3 6.4 2.4 4.9 30 2.5 40 0.6 0.6 1.5 1.6 7.7 8.6 9.5 50 2.7 5.2 5.5 5.8 5.9 10.1 2.8 0.6 1.6 2.8 10.2 8.9 11.0 12.2 13.8 14.7 15.3 120 7.4 11.3 14.4 16.6 19.0 20.5 21.1 (a) What are the meanings of the partial derivatives əh/av and əh/at? (b) Estimate the values of f(40, 15) and fi(40, 15). What are the practical interpretations of these values?
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