The temperate at a point (x, Y, Z) [s given by TC, Y) z)= 200e^?-5y2-9z? where Tis measured in°C and X, Y, Z in meters. al Find the rate of change of temporature at the pornt P(2,-1,4) in the directven towards' the peint C3,-4,6). ) In whreh directron does the te mperature merease fastest at P?, O Fmd the maximum rarte of inerease at P.
The temperate at a point (x, Y, Z) [s given by TC, Y) z)= 200e^?-5y2-9z? where Tis measured in°C and X, Y, Z in meters. al Find the rate of change of temporature at the pornt P(2,-1,4) in the directven towards' the peint C3,-4,6). ) In whreh directron does the te mperature merease fastest at P?, O Fmd the maximum rarte of inerease at P.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The temperature at a point \((x, y, z)\) is given by:
\[ T(x, y, z) = 200e^{-x^2 - 5y^2 - 9z^2} \]
where \(T\) is measured in °C and \(x, y, z\) in meters.
a) Find the rate of change of temperature at the point \(P(2, -1, 4)\) in the direction towards the point \((3, -4, 6)\).
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%2F66de1f81-f5e7-4658-9693-a6a0d6d0d266%2F3db49b26-43fa-4893-a689-0f55d4eaa635%2Fwv7d7sa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The temperature at a point \((x, y, z)\) is given by:
\[ T(x, y, z) = 200e^{-x^2 - 5y^2 - 9z^2} \]
where \(T\) is measured in °C and \(x, y, z\) in meters.
a) Find the rate of change of temperature at the point \(P(2, -1, 4)\) in the direction towards the point \((3, -4, 6)\).
b) In which direction does the temperature increase fastest at \(P\)?
c) Find the maximum rate of increase at \(P\).
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