=) Find the directional derivative at the point P = (2, 1, 1) of the scalar function in the direction perpendicular to the level surface t = -1 at the point Q=(-1,1,0).

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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Needed to be solved part C correctly in 30 minutes and get the thumbs up please show neat and clean work
1) Consider
(x, y, z) = 2xyz - x²y³
v(x, y, z) = xy² + y sin(z)
F(x, y, z) = F₂(x, y, z)i + F₂(x, y, z)j + F(x, y, z)k
(a) Calculate
1. Vo
ii. V²
iii. V. (V x F)
(b) At the point P = (1,3,0) calculate the directions in which the function
does not change.
(c) Find the directional derivative at the point P (2, 1, 1) of the scalar
function in the direction perpendicular to the level surface t = -1 at
the point Q=(-1,1,0).
=
Transcribed Image Text:1) Consider (x, y, z) = 2xyz - x²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z) = F₂(x, y, z)i + F₂(x, y, z)j + F(x, y, z)k (a) Calculate 1. Vo ii. V² iii. V. (V x F) (b) At the point P = (1,3,0) calculate the directions in which the function does not change. (c) Find the directional derivative at the point P (2, 1, 1) of the scalar function in the direction perpendicular to the level surface t = -1 at the point Q=(-1,1,0). =
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