The temperature at a point (x, y, z) is given by じ -x²–2y²–22 T(x, y, z) = 1000e where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -2, 2) in the direction toward the point Q(3, –4, 3). f(2, –2, 2) = PQ Answer: D-→ 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
The temperature at a point (x, y, z) is given by じ -x²–2y²–22 T(x, y, z) = 1000e where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -2, 2) in the direction toward the point Q(3, –4, 3). f(2, –2, 2) = PQ Answer: D-→ 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
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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Transcribed Image Text:The temperature at a point (x, y, z) is given by
T(x, Y, z)
1000e
-x²–2y²-22
where T is measured in °C and x, y, and z in meters.
1. Find the rate of change of the temperature at the point P(2, -2, 2) in the direction toward the
point Q(3, –4, 3).
Answer: D f(2, –2, 2)
PQ
2. In what direction does the temperature increase fastest at P?
Answer:
3. Find the maximum rate of increase at P.
Answer:
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