Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 11.6, Problem 54PS
(a)
To determine
To verify: The given property for the function of two variables.
(b)
To determine
To verify: The given property for the function of two variables.
(c)
To determine
To verify: The given property for the function of two variables.
(d)
To determine
To verify: The given property for the function of two variables.
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A ball is tossed upward from a tall building, and its upward velocity V, in feet per second, is a function of the time t, in seconds, since the ball was thrown. The formula is
V = 56 - 32r
if we ignore air resistance. The function Vis positive when the ball is rising and negative when the ball is falling.
(a) Express using functional notation the velocity 1 second after the ball is thrown, and then calculate that value.
])=24
✔ft per sec
Is the ball rising or falling then?
Because the upward velocity is positive, the ball is rising.
O Because the upward velocity is positive, the ball is falling.
O Because the upward velocity is negative, the ball is rising.
O Because the upward velocity is negative, the ball is falling.
(b) Find the velocity 2 seconds after the ball is thrown.
✔ft per sec
8
Is the ball rising or falling then?
O Because the upward velocity is positive, the ball is rising.
ⒸBecause the upward velocity is positive, the ball is falling.
O Because the upward velocity is…
An airport can be cleared of fog by heating the air. The amount of heat required depends on the air temperature and the wetness of the fog. The figure
below shows the heat H(T, w) required (in calories per cubic meter of fog) as a function of the temperature T (in degrees Celsius) and the water content w (in
grams per cubic meter of fog). Note that this figure is not a contour diagram, but shows cross-sections of H with w fixed at 0.1, 0.2, 0.3, and 0.4.
H(T,8.4)
500
H(T,8.3)
B00
H(T,8.2)
200
100
H(T,8.1)
(a) Estimate HT(10,0.2):
HT(10,0.2)
(Be sure you can interpret this partial derivative in practical terms.)
(b) Make a table of values for H(T, w) from the figure, and use it to estimate HT(T, w) for each of the following:
Т%3 20, w — 0.2: Нт(Т, w)
T = 30, w = 0.2 : HT(T, w) =
T = 20, w = 0.3 : HT(T,w) z
T = 30, w = 0.3 : HT(T, w) 2
An airport can be cleared of fog by heating the air. The amount of heat required depends on the air temperature and the wetness of the fog. The figure below shows the heat H(T,w) required (in calories per cubic meter of fog) as a function of the temperature T (in degrees Celsius) and the water content w (in grams per cubic meter of fog). Note that this figure is not a contour diagram, but shows cross-sections of H with w fixed at 0.1, 0.2, 0.3, and 0.4.
(a) Estimate HT (10,0.2): HT (10,0.2) ≈ (Be sure you can interpret this partial derivative in practical terms.)
(b) Make a table of values for H(T,w) from the figure, and use it to estimate HT (T,w) for each of the following: T = 20,w = 0.2 : HT (T,w) ≈ T = 30,w = 0.2 : HT (T,w) ≈ T = 20,w = 0.3 : HT (T,w) ≈ T = 30,w = 0.3 : HT (T,w) ≈
(c) Repeat (b) to find Hw(T,w) for each of the following: T = 20,w = 0.2 : Hw(T,w) ≈ T = 30,w = 0.2 : Hw(T,w) ≈ T = 20,w = 0.3 : Hw(T,w) ≈ T = 30,w = 0.3 : Hw(T,w) ≈ (Be sure you can interpret this…
Chapter 11 Solutions
Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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