The temperature at a point (a, Y, z) is given by T(x, y, z) = 100e-2-y²-722 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(4,-1,4) in the direction toward the point Q(6, -4, 5) (b) In which direction does the temperature increase fastest at P?
The temperature at a point (a, Y, z) is given by T(x, y, z) = 100e-2-y²-722 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(4,-1,4) in the direction toward the point Q(6, -4, 5) (b) In which direction does the temperature increase fastest 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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Transcribed Image Text:Q1.
The temperature at a point (x, y, z) is given by
T(x, y, z) = 100e¬ª²-y²-72²
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(4, –1, 4) in the direction
toward the point Q(6, -4, 5)
(b) In which direction does the temperature increase fastest at P?
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