The temperature at a point (x,y,z) is given by T(x, y, z) = 200e-4-²9, where T is measured i degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (4, -3, 4). In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)? ( What is the maximum rate of increase of T at (1, 1, -1)?
The temperature at a point (x,y,z) is given by T(x, y, z) = 200e-4-²9, where T is measured i degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (4, -3, 4). In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)? ( What is the maximum rate of increase of T at (1, 1, -1)?
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:The temperature at a point (x,y,z) is given by T(x, y, z) = 200e-²-²/4-2²/9, where I is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track
of what needs to be a unit vector.
Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (4, -3, 4).
In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)?
What is the maximum rate of increase of T at (1, 1, -1)?
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