Please answer both questions. Thank you. Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction in which it occurs.Maximum rate of change:Direction (unit vector) in which it occurs: Suppose that distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distancefrom a fixed point, which we take to be the origin. Suppose that the temperature 1 lightyear from the origin is 1000 degrees celsius. Findthe gradient of T at (x, y, z).VT = (Note: Your answers should be expressions of x, y and z; e.g. "3x - 4yz"

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Description: Please answer both questions. Thank you. Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction in which it occurs.Maximum rate of change:Direction (unit vector) in which it occurs: Suppose that distances a

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Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs:

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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Please answer both questions. Thank you.

Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction in which it occurs.
Maximum rate of change:
Direction (unit vector) in which it occurs:

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"

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