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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with c-e! Thank you!
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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