Problem #5:Use the divergence theorem to find the outward fluxF.n dSof the vector fieldFtan (7y + 10z) i + e²² + 6 cOs x¡ + Vx² +v² + z² k, where S is the surface of the region.22.bounded by the graphs of z =x² + v² and x² + y² + z2 = 100.

Answered: Image /qna-images/answer/f807c37c-4126-4b3f-8375-c67423b4b0df.jpg

Answered: "roblem #5: Use the divergence theorem…

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

Compute the curl of the vector field F = (xy+ z²,x², xz – 2). curl(F(x, y, z)) = What is the curl at the point (0, -1,0)? curl(F (0, – 1,0)) = Is this vector field irrotational or not v OChoose irrotational not irrotational ct. cannot be determined
Show the vector field V = (8xy³z, 12x²y² z, 4x²y³) is irrotational, and find its potential. Then, by using the Path Independence Integral, and the Fundamental Theorem of Calculus for Vector Fields evaluate the line integral along the helix parameterized by r(t) = (2 cos t, 2 sint, t) from (2, 0, 0) to (1, √3, π/3)
3. Use the divergence of the vector field to compute Y F(x, y) 2²1) ₁ + (29-2 +²8²) J = fo tan -1 tan 4 -1 (2x) dy - where C is the cardiod r= 1+ sin 0. (ry. Y 2+82, dx,
6. Consider the vector field F(ar, y) = (8r°y+ e")î+ (Ka + e")3, where K is some constant. (a) (5 points) For which value of K is F the gradient of a function? For this value, find f such that F = Vf. (b) (5 points) For the value of K found in part (a), evaluate fe F dr, where C is the segment of the curve y = a from (0,0) to (1, 1). (c) (5 points) If instead K = 1, use Green's Theorem to evaluate f F dr, where C is the boundary of the triangle with vertices (0,0), (2,0), and (2, 1), traversed counterclockwise.
Use the divergence of the vector field to compute F(x,0) = (tan 1(2x))i + (x3-2+8³) y) xy 4 fta (22) dy - (zy-2-54²) dr. tan¯¹ 4 xy dx, 2+8x² where C is the cardiod r = 1 + sin 0. j
Find the scalar potential for the conservative field: F(x, y, z) = 12xyi + (6x² − 6z²)j + (−12zy +9)k The scalar potential is $(x, y, z) = ¯ +C Use this fact to evaluate Jo curve joining the points P = (3,3,0) and Q = (0, -3, -4). [B C F. dr = 0 F. dr where C is a smooth
a) Find the values of a,b,c which make f(x,y,z) = sin (xay°z©) a potential function for the vector field F(x.y,z)= 4 x³y'z? cos (x*y z7) i+ 7x*y®z7 cos (x*y'z?) j + 7x*y?z® cos (x*y'z7) k a= b= c= b) Find the work of F along the curve r(t)=(2t, e t(t – 1), e tt – 1)) for 0sts1. Do not approximate your answer. For example, leave sin (e ) as that, not 0.41. Work = F•dr =

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

"roblem #5: Use the divergence theorem to find the outward flux F.n dS of the vector field F = tan(7y + 10z) i + e + 6 cos xj + Vx2 + y² + z² k, where S is the surface of the region Vx² + y² and x2 + y? + z2 bounded by the graphs of z = = 100.