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...

See similar textbooks

Similar questions

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
2. For the vector field F (x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div (F)div (F) (b) curl (F)curl(F) (c) div (curl (F))
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…
4. Match the vector fields given below with their plots. (a) F(x, y, z) = (b) F(x, y, 2) = (c) F(x, Y, z) = x² + y² (d) F(x, y, z) = (x² + y² + z²)3/2’ (x² + y² + z²)3/2' (x² + y² + 2²)3/2 Field (I) Field (II) Field (III) Field (VI)
Suppose F(x, y) = x² + y² and C is the line segment from point A = (1, −1) to B = (3, −5). (a) Find a vector parametric equation (t) for the line segment C so that points A and B correspond to t= 0 and t = 1, respectively. F(t) = = (b) Using the parametrization in part (a), the line integral of along C' is dt LE · dF = [ ° F (F(t)) - 7"' (t) dt = √° with limits of integration a = and b = (c) Evaluate the line integral in part (b).
Let F₁ (x, y, z) = (y, x − z² +2,−2yz) and F₂ (x, y, z) = (x − z², −y + 2, 2yz). (a) Find the curl of each vector field. (b) Which of these two vector fields is conservative? Find a potential function for the one that is. (c) Let F be either F₁ or F2 (whichever you want), and let C denote the curve shown in the figure which starts at the point (0, 1,0), stays above the circle x² + y² = 1 and spirals upwards in a clockwise direction to the point (0,1,1). Jo Find the exact value of the line integral: F. dr.
a) Show that F (x, y) = (yexy + cos(x + y)) i + (xexy + cos(x + y) j is the gradient of some function f. Find f b) Evaluate the line integral ʃC F dr where the vector field is given by F (x, y) = (yexy + cos(x + y)) i + (xexy + cos(x + y) j and C is the curve on the circle x 2 + y 2 = 9 from (3, 0) to (0, 3) in a counterclockwise direction.
Find the outward flux of F = (4x + 25y²,0. 10z through the surface 3 = 1. 25 4
h) Given vector field F (x, y, z) = (2x + 2y + 42) i + (2y +2x –. - 32) + (2z – 3y + 4x) k. 4. (a) Prove or disprove that f(x, Y, z) = x² + y² + z² + 2xy – 3yz + 4xz is a potential function for vector field F. (b) Find ſ, Fdr, where L is a part of the helix x = connecting the points A(3,0, 1) and (-3,0, 2) 3 cos (rt), у = 3 sin(rt), z =1+t, 0 < t < 1,
Sketch the vector field F(x, y) = x3, the line segment from (1, 3) to (9, 3), and the line segment from (3,5) to (3,9). (a) Calculate the line integral of the vector field F along the line segment from (1, 3) to (9, 3). (b) Calculate the line integral of the vector field F along the line segment from (3, 5) to (3, 9).

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS