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The temperature at a point (x, y, z) is given by 400ex-3y2- 9z2 --_ (x, y, z) 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, 2) in the direction towards the point (5, -5, 6) oc/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 400ex-3y2- 9z2 --_ (x, y, z) 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, 2) in the direction towards the point (5, -5, 6) oc/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

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) = 400e−x2 − 3y2 − 9z2

where T is measured in °C and

x, y, z

in meters.

The temperature at a point (x, y, z) is given by 400ex-3y2- 9z2 --_ (x, y, z) 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, 2) in the direction towards the point (5, -5, 6) oc/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
Transcribed Image Text:The temperature at a point (x, y, z) is given by 400ex-3y2- 9z2 --_ (x, y, z) 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, 2) in the direction towards the point (5, -5, 6) oc/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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