The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 5y29z2 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -3, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 5y29z2 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -3, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
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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a,b,c please
Transcribed Image Text:The temperature at a point (x, y, z) is given by
T(x, y, z) = 100e-x² - 5y² - 9z²
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -3, 6).
°C/m
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.
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