Consider 23 (x, y, z) = 10xyz - 4x²y³ v(x, y, z) = 4xy² + 3y sin(2) Ğ(x, y, z) = Gx(x, y, z)i + Gy(x, y, z)j + Gz(x, y, z)k (a) Calculate i. Vo ii. V2 iii. V. (V×G) (b) At the point P = (1,2, 0) calculate the directions in which the function of does not change. (c) Find the directional derivative at the point P = (1, 2, 0) of the scalar function in the direction perpendicular to the level surface & = -4 at the point Q = (-1, 1, 0).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
Question
Consider
23
(x, y, z) = 10xyz - 4x²y³
v(x, y, z) = 4xy² + 3y sin(2)
Ğ(x, y, z) = Gx(x, y, z)i + Gy(x, y, z)j + Gz(x, y, z)k
(a) Calculate
i. Vo
ii. V2
iii. V. (V×G)
(b) At the point P = (1,2, 0) calculate the directions in which the function of
does not change.
(c) Find the directional derivative at the point P = (1, 2, 0) of the scalar
function in the direction perpendicular to the level surface & = -4 at
the point Q = (-1, 1, 0).
Transcribed Image Text:Consider 23 (x, y, z) = 10xyz - 4x²y³ v(x, y, z) = 4xy² + 3y sin(2) Ğ(x, y, z) = Gx(x, y, z)i + Gy(x, y, z)j + Gz(x, y, z)k (a) Calculate i. Vo ii. V2 iii. V. (V×G) (b) At the point P = (1,2, 0) calculate the directions in which the function of does not change. (c) Find the directional derivative at the point P = (1, 2, 0) of the scalar function in the direction perpendicular to the level surface & = -4 at the point Q = (-1, 1, 0).
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