The temperature at a point (x, y, z) is given by the following equation where T is measured in °C and x, y, z in meters. T(x, y, z) = 200e-x²-3y²-9z² (a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3). -10400 6 43 °C/m (b) In which direction does the temperature increase fastest at P? -18 <-2, 3 (c) Find the maximum rate of increase at P. -43√337 400e
The temperature at a point (x, y, z) is given by the following equation where T is measured in °C and x, y, z in meters. T(x, y, z) = 200e-x²-3y²-9z² (a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3). -10400 6 43 °C/m (b) In which direction does the temperature increase fastest at P? -18 <-2, 3 (c) Find the maximum rate of increase at P. -43√337 400e
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 the following equation where T is measured in ºC and x, y, z in meters.
T(x, y, z) = 200e-x²-3y²-9z²
(a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3).
-10400
43√6
°C/m
(b) In which direction does the temperature increase fastest at P?
<-2, 3
-18
(c) Find the maximum rate of increase at P.
-43
400e
3√337
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