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c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of r, f(r+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.

c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of r, f(r+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 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 5 10 15 20 25 30 35 40 -25 -46 -40 -53 -47 -58 -51 -61 -55 -64-58 -67-60 -69 -62 -71 -64 -20 -15 -10 -5 0 -34 -28 -22 -16 -11 -16 -41 -35 -28 -22 -45 -42 -35 -29 -48 -39 -32 -26 -51 -44 -37-31 -33 -53 -46 -39 -48 -41 -34 -55 -57 -50 -43 -36 5 -5 -10 -19 -13 -22 -15 -24 -17 -26 -19 -27 -21 -14 -7 -29 -22 -15 -8 10 15 1 7 -4 3 -7 0 -9 -2 4 -11 -4 3 -12 -5 1 58 20 13 9 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(zh) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h w (25-10)-W(15, -10) = -37 - (-32) 2 (5) 10 w (20,-5) _w (20, -15) 2 (5) 0 -1 W. (20,-101-1 b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? d. Use your results to estimate the wind chill w(20, -12). c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of r, f(a+h)≈ f(x) + hf'(x).) ==// 1--29-(-42) = 13 °F -15) --29 FF 10 e. Consider how you might combine your previous results to estimate the wind chill w(18,-12). Explain your process. Units. Pe Per
Transcribed Image Text:CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 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 5 10 15 20 25 30 35 40 -25 -46 -40 -53 -47 -58 -51 -61 -55 -64-58 -67-60 -69 -62 -71 -64 -20 -15 -10 -5 0 -34 -28 -22 -16 -11 -16 -41 -35 -28 -22 -45 -42 -35 -29 -48 -39 -32 -26 -51 -44 -37-31 -33 -53 -46 -39 -48 -41 -34 -55 -57 -50 -43 -36 5 -5 -10 -19 -13 -22 -15 -24 -17 -26 -19 -27 -21 -14 -7 -29 -22 -15 -8 10 15 1 7 -4 3 -7 0 -9 -2 4 -11 -4 3 -12 -5 1 58 20 13 9 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(zh) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h w (25-10)-W(15, -10) = -37 - (-32) 2 (5) 10 w (20,-5) _w (20, -15) 2 (5) 0 -1 W. (20,-101-1 b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? d. Use your results to estimate the wind chill w(20, -12). c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of r, f(a+h)≈ f(x) + hf'(x).) ==// 1--29-(-42) = 13 °F -15) --29 FF 10 e. Consider how you might combine your previous results to estimate the wind chill w(18,-12). Explain your process. Units. Pe Per
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