For number 9The answer is ACould you show me how equals:(A) 0(B) 2πi/9(C) -2π/3-2πi/9(D) 1/99 The outward flux of the vector field F(x, y, z) = (1/2 + e+e+z(A) 2πthe boundary of the region E = {(x, y, z) = R³: x² + y²+z2 <4, y ≥0, z> 0} is22, ex+z+e+y2through(B) T(C) -π(D) 2√210 Consider the vector field F(x, y, z) = (±±±², 5, +2²)ThenN =defined on the set= {(x, y, z) = R³:-5

Answered: Image /qna-images/answer/d20764b5-9211-4949-a1fd-b009bfec5253.jpg

Answered: equals: (A) 0 (B) 2πi/9 (C) -2π/3-2πi/9…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The gradient vector field of f(x,y)=cos(x) - 2sin(y) is: O1. f(x,y)= cos(x) i - 2sin(y) j II. f(x,y)=-sin(x) i - 2cos(y) j III. f(x,y)= sin(x) i - 2cos(y) j IV. f(x,y)=-sin(x) i+ 2cos(y) j
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Vector Field F = 6xi + (2y – y²)j+(6z – x³)k is Conservative Select one: True False
Determine whether or not the given vector field F is conservative. If so, find a potential function. (a) F(x, y) = (x, y) (b) F(x, y) = (3x²y, x³ (c) F(x, y) = (2xe" + y, x² e +x - 2y) (d) F(x, y) = (siny - y sin x+x, cos x + x cos y + y) (e) F(x, y) = (sin(xy) + xy cos(xy), x² cos(xy)) (f) F(x, y, z) = (x, y, z) - (g) F(x, y, z) = (x + 2, −y - z, x − y) (h) F(x, y, z) = (2xy³, x²z³, 3x²yz²) (i) F(x, y, z) = (3y4z2, 4x³ z², -3x²y²) (j) F(x, y, z) = (2x² + 8xy², 3x³y - 3xy, -4y² z² - 2x³z) (k) F(x, y, z) = (y² cosx+23, -4+ 2y sin x, 3xz² + 2) (1) F(x, y, z) = (4xy - 3x²x² + 1,2x² + 2, −2x³z+3z²) Linear vector fields (a) On R² with coordinates x, y, define a vector field to be linear if it is given by a matrix formula = M + V a = -635+6-2+3+; C M = ax+by+e [cx + dy+f] Find necessary and sufficient conditions for to be conservative. Prove that the conditions you wrote are correct. (b) Repeat for a vector field in R3 (using a 3 × 3 matrix in place of M and a 3 × 1 column vector in place of…
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