Problem #4:Problem #4:Use the divergence theorem to find the outward fluxof the vector fieldF = tan-l(7y + 8z)i + ez+6cosXj + √²+² +2² k, where S is the surface of the region bounded by thegraphs of z = √√x2 + y² and x² + y² +22² = 100.SS FEnter your answer symbolically,as in these examplesFindS

The given problem is to find the flux of the given vector over the given surface bounded by given…

Answered: Problem #4: Problem #4: SS F Use the…

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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9. Find the flux of the vector field B(x, y,z) shown in the left figure through the square S of side 2 shown in the right figure , oriented in the j direction, where B(x, v. z)== yi +xj x²+y² S + 2 1 3
8. Use (a) parametrization; (b) Stokes' Theorem to compute fF.dr for the vector field F = (x²+z)i + (y² + 2x)j + (z² −y)k and the curve C which is the intersection of the sphere x² + y² +2²=1 with the cone z = √² + y² in the counterclockwise direction as viewed from above. -
17. Verify Stokes's Theorem for the following vector field E = xyâ – (x² + 2y²)ây - for the contour shown below. Recall Stokes's Theorem: Ē - ai = [[ (v x E) · dš E di || (v x E) · dš C S y
The task is to answer the question below: Given that C₁ be the directed line segment from (2, 0)to (−2, 0)and C₂ be the upper half of the circle x² + y² = 4 oriented clockwise. Let C C₁ U C₂ and consider the vector field F~ (x, y) = (xy² + e²x − 3y₁x²y - siny). (a) Evaluate F.dR C₁
Problem 1: For the scalar fields below, determine the unit vector pointing in the direction of maximum possible change of the function a) f(x,y,z) = x + y? + z³ b) f(r, p, z) = r² sin(4) + z²
Calculate the circulation of the field F around the closed curve C. Circulation means line integralF = x 3y 2 i + x 3y 2 j; curve C is the counterclockwise path around the rectangle with vertices at (0,0),(3,0).(3,2) and (0.2)
Find all the potential functions, if there are any, of the vector field F(x, y, z) = (2x sin(y — 42) + 3y²e²y², æ² cos(y − 42) + 6xyeªy² + 5y¹, −4x² cos(y – -42)).
19. Consider the vector field V(r, y, 2) = 1-y |x²+(y-1)² > x²+(y-1)² (y: H) and the curves C1 : x² + (y – 1)2 = 1, 62 : x² + (y – 2)² = 4 and 63 : x² + (y – 4)² = 1. (a) Compute V• dr.

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