Suppose that distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which we take to be the origin. Suppose that the temperature 1 lightyear from the origin is 1000 degrees celsius. Find the gradient of T at (x, y, z). VT = ( Note: Your answers should be expressions of x, y and z; e.g. "3x - 4yz"

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose that distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distance from a
fixed point, which we take to be the origin. Suppose that the temperature 1 lightyear from the origin is 1000 degrees celsius. Find the gradient
of T at (x, y, z).
VT = (
Note: Your answers should be expressions of x, y and z; e.g. "3x - 4yz"
Transcribed Image Text:Suppose that distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which we take to be the origin. Suppose that the temperature 1 lightyear from the origin is 1000 degrees celsius. Find the gradient of T at (x, y, z). VT = ( Note: Your answers should be expressions of x, y and z; e.g. "3x - 4yz"
Find the directional derivative of f(x, y, z) = –1æ² + 5y? – 122 at the point (4, 5, -2) in the direction of the origin.
Transcribed Image Text:Find the directional derivative of f(x, y, z) = –1æ² + 5y? – 122 at the point (4, 5, -2) in the direction of the origin.
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