Consider the following equation. f(x, y) = sin(4x + 5y), P(-15, 12), u =(√31-1) (a) Find the gradient of f. Of(x, y) = (b) Evaluate the gradient at the point P. V(-15, 12) = (c) Find the rate of change of f at P in the direction of the vector u. D-15, 12) =

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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Consider the following equation.
f(x, y) = sin(4x + 5y), P(-15, 12), u =(√31-1)
(a) Find the gradient of f.
Vf(x, y) =
(b) Evaluate the gradient at the point P.
Vf(-15, 12) =
(c) Find the rate of change of f at P in the direction of the vector u.
Du f(-15, 12) =
Transcribed Image Text:Consider the following equation. f(x, y) = sin(4x + 5y), P(-15, 12), u =(√31-1) (a) Find the gradient of f. Vf(x, y) = (b) Evaluate the gradient at the point P. Vf(-15, 12) = (c) Find the rate of change of f at P in the direction of the vector u. Du f(-15, 12) =
Find the directional derivative of the function at the given point in the direction of the vector v.
f(x, y, z) = xey + ye² + zex, (0, 0, 0), v = (6, 1, -2)
D(0, 0, 0) =
Transcribed Image Text:Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xey + ye² + zex, (0, 0, 0), v = (6, 1, -2) D(0, 0, 0) =
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