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The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-²-S2-922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in "C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4). C/m

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-²-S2-922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in "C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4). C/m

Advanced Engineering Mathematics
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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The temperature at a point (x, y, z) is given by T(x, y, z)= 100e-²-Sy2 - 922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in °C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4). C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. Need Help? Read It
Transcribed Image Text:The temperature at a point (x, y, z) is given by T(x, y, z)= 100e-²-Sy2 - 922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in °C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4). C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. Need Help? Read It
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