PLEASE ANSWER ALL PARTS AND SHOW WORK. THANK YOU!
PLEASE ANSWER ALL PARTS AND SHOW WORK. THANK YOU! If F is a continuous vector field...
3. If S is a sphere, and F is a vector field that fulfills the hypotheses of Stokes' Theorem, then what is the value of curl F dS? (d) It cannot be determined without knowing F. (e) None of the other choices 4. True or False? Suppose that Si and S2 are oriented piecewise-smooth surfaces that share the same simple, closed, piecewise-smooth boundary curve C. Let F be a vector field whose components have continuous partial derivatives on an open...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
1. Consider the vector field z, y, z) = 〈re,zz,H) and the surface s in the figure below oriented outward. Unit circle Use Stokes' Theorem in two different ways to find/curl F dS, by: (a) [7 pts.] evaluating ф F-dr where C in the positively oriented unit circle in the figure (which is the boundary of S), (b) [7 pts.] evaluating curl F dS, where Si is the upward oriented unit disc bounded by C 1. Consider the vector field...
Show all work and use correct notation for full credit. Stokes' Theorem: Let S be an orientable, piecewise smooth surface, bounded by a simple closed piecewise smooth curve C with positive orientation. Let F be a vector field with component functions that have continuous partial derivatives on an open region in R3 that contains S. Then | | curl(F) . ds F-dr = where curl(F) = ▽ × F. (2 Credits) Let S be the cone given by {(z, y,...
Please show all the work to complete the question and explain each step, please. Thank you! Let F(x, y) e*y (y cos x - centered at (1,0) in the first quadrant, traced clockwise from (0,0) to (2, 0). And suppose that C2 is the line from (0,0) to (2,0). sin x) xexy cos xj. Suppose that C1 is the half of the unit circle (A) Use the curl test to determine whether F is a gradient vector field or not....
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
answer all parts please except A if you cannot (6) Consider the vector field F(x,y)-《22, 3y). A path is closed if it ends whiere it starts Consider the 3 closed paths starting and ending at (3,0): C1 the circle of radius 3 centered at the origin, C2 the ellipse with equation 2 +3y2-9, and Cs the flat linear path going to -3 and then going straight back. (a) Use GeoGebra to plot the vector field F (b) For each, parametrize...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-2ǐ + 2xk and the surface S the part of the paraboloid z = 20-x2-y2 that lies above the plane z = 4, oriented upwards. To verify Stokes' Theorem we will compute the expression on each side. First computel curl F dS curl F- curl F. dS- EEdy di where curl F dS- Now compute F dr The boundary curve C of the...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
Verify that Stokes' Theorem is true for the vector field Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...