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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0733446e-3a29-4244-a004-4a90c33cdc78%2Fbbb5bc1d-a5c2-4c96-8297-ac49512ba3c9%2F16lghsc.png&w=3840&q=75)
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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