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CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 58 Activity 10.2.5 The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. In Table 10.2.3, the wind chill w, measured in degrees Fahrenheit, is a function of the wind speed v, measured in miles per hour, and the ambient air temperature T, also measured in degrees Fahrenheit. We thus view w as being of the form w=w(v, T). Table 10.2.3 Wind chill as a function of wind speed and temperature. v\T -30 -25 -20 -15 -10 -5 0 5 5 10 -53 -46 -40 -34 -28 -22 -16 -11 -5 -47 -41 -35 -28 -22 -16 -58 -51 -45 -39 -32 -26 -19 20 -61 -55 -48 <-42 15 25 -64 -58 -51 -44 30 -67 -60 -53 -46 35 -69 -62 -55 -48 -41 -71-64 -57 -50 -43 40 10 15 20 1 7 13 -10 -4 3 9 -13 -7 0 6 -15 -9 -2 4 -37 -35 <-29 -22 -31 -24 -17 -11 -4 -26 -19 -12 -5 1 3 -39 -33 -34 -27 -21 -14 -7 0 -36-29 -22 -15 -8 -1 a. Estimate the partial derivative w, (20,-10). What are the units on this quantity and what does it mean? (Recall that we can estimate a partial derivative of a single variable function f using the symmetric difference quotient (z+h)-f(-) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of z, f(a+h) f(x) + hf'(x).) d. Use your results to estimate the wind chill w(20, -12). e. Consider how you might combine your previous results to estimate the wind chill w(18, -12). Explain your process.

CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 58 Activity 10.2.5 The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. In Table 10.2.3, the wind chill w, measured in degrees Fahrenheit, is a function of the wind speed v, measured in miles per hour, and the ambient air temperature T, also measured in degrees Fahrenheit. We thus view w as being of the form w=w(v, T). Table 10.2.3 Wind chill as a function of wind speed and temperature. v\T -30 -25 -20 -15 -10 -5 0 5 5 10 -53 -46 -40 -34 -28 -22 -16 -11 -5 -47 -41 -35 -28 -22 -16 -58 -51 -45 -39 -32 -26 -19 20 -61 -55 -48 <-42 15 25 -64 -58 -51 -44 30 -67 -60 -53 -46 35 -69 -62 -55 -48 -41 -71-64 -57 -50 -43 40 10 15 20 1 7 13 -10 -4 3 9 -13 -7 0 6 -15 -9 -2 4 -37 -35 <-29 -22 -31 -24 -17 -11 -4 -26 -19 -12 -5 1 3 -39 -33 -34 -27 -21 -14 -7 0 -36-29 -22 -15 -8 -1 a. Estimate the partial derivative w, (20,-10). What are the units on this quantity and what does it mean? (Recall that we can estimate a partial derivative of a single variable function f using the symmetric difference quotient (z+h)-f(-) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of z, f(a+h) f(x) + hf'(x).) d. Use your results to estimate the wind chill w(20, -12). e. Consider how you might combine your previous results to estimate the wind chill w(18, -12). Explain your process.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 58 Activity 10.2.5 The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. In Table 10.2.3, the wind chill w, measured in degrees Fahrenheit, is a function of the wind speed v, measured in miles per hour, and the ambient air temperature T, also measured in degrees Fahrenheit. We thus view w as being of the form w=w(v, T). Table 10.2.3 Wind chill as a function of wind speed and temperature. v\T -30 -25 10 15 20 5 -46 -40 1 7 13 10 -53 -47 -4 3 9 15 -13 -7 0 -20 -15 -10 -5 0 5 -34 -28 -22 -16 -11 -5 -41 -35 -28 -22 -16 -10 -58 -51 -45 -39 -32 -26 -19 20 -61 -55 -48 -42 -35 -35 -29 -22 -15 25 -64-58 -58 -51 -44 -37 -31 -24 -17 -11 -4 3 30 -67 -60 -53 -46 -39 -33 -26 -19 -12 -5 1 35 -69 -62 -55 -48 -41 -34 -21 -14 -7 0 -71 -64 -57 -50 -43 -36 -29 -22 -15 -8 -1 -9 -24 -27 40 6 a. Estimate the partial derivative w, (20,-10). What are the units on this quantity and what does it mean? (Recall that we can estimate a partial derivative of a single variable function f using the symmetric difference quotient f(a+h)-f(-h) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of z, f(a+h) f(x) + hf'(x).) d. Use your results to estimate the wind chill w(20, -12). e. Consider how you might combine your previous results to estimate the wind chill w(18, -12). Explain your process.
Transcribed Image Text:CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 58 Activity 10.2.5 The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. In Table 10.2.3, the wind chill w, measured in degrees Fahrenheit, is a function of the wind speed v, measured in miles per hour, and the ambient air temperature T, also measured in degrees Fahrenheit. We thus view w as being of the form w=w(v, T). Table 10.2.3 Wind chill as a function of wind speed and temperature. v\T -30 -25 10 15 20 5 -46 -40 1 7 13 10 -53 -47 -4 3 9 15 -13 -7 0 -20 -15 -10 -5 0 5 -34 -28 -22 -16 -11 -5 -41 -35 -28 -22 -16 -10 -58 -51 -45 -39 -32 -26 -19 20 -61 -55 -48 -42 -35 -35 -29 -22 -15 25 -64-58 -58 -51 -44 -37 -31 -24 -17 -11 -4 3 30 -67 -60 -53 -46 -39 -33 -26 -19 -12 -5 1 35 -69 -62 -55 -48 -41 -34 -21 -14 -7 0 -71 -64 -57 -50 -43 -36 -29 -22 -15 -8 -1 -9 -24 -27 40 6 a. Estimate the partial derivative w, (20,-10). What are the units on this quantity and what does it mean? (Recall that we can estimate a partial derivative of a single variable function f using the symmetric difference quotient f(a+h)-f(-h) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of z, f(a+h) f(x) + hf'(x).) d. Use your results to estimate the wind chill w(20, -12). e. Consider how you might combine your previous results to estimate the wind chill w(18, -12). Explain your process.
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