(curl F) n dS Use Stokes' Theorem to calculate 8) F-5yi - 6xj + 2z^k; C: the portion of the plane 6x + 7y + 4z -6 in the first quadrant A) B) 0 C) -11 D) 7 (curl F) n dS Use Stokes' Theo...
. Problem #8: Use Stokes' Theorem to evaluate | F• dr where F = (x + 52)i + (6x + y)j + (7y - -)k and C is the curve of intersection of the plane x + 3y += = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) Problem #8: Just Save Submit Problem #8 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #8 Your Answer: Your Mark:...
Use Stokes' Theorem (in reverse) to evaluate Sf (curl F). n ds where F = 5yzi + 9x j +2yze+'k ,S is the portion of the paraboloid z = x2 + aby2 for 0 sz s 3, and the unit normal on S points away from the z-axis. 16 Enter your answer symbolically, as in these examples
Problem #2: Д eн (curl F) n dS where Use Stokes' Theorem (in reverse) to evaluate 10yze normal on S points away from the z-axis k ,S is the portion of the paraboloid 7yzi Зxј F for 0 s z s 2, and the unit + Z = 16 + 64 = Enter your answer symbolically, as in these examples Problem #2: Just Save Submit Problem #2 for Grading Attempt #3 Attempt #4 Problem #2 Attempt 1 Attempt #2 Attempt...
Problem #9: Use Stokes' Theorem (in reverse) to evaluate Sf (curl F). n ds where F = 7yzi + 9x j +6yzet k ,S is the portion of the paraboloid z = 36 x? normal on S points away from the z-axis. + for 0 sz s 4, and the unit 64. -3648*pi Enter your answer symbolically, as in these examples Problem #9: -36481 Just Save Submit Problem #9 for Grading Problem #9 Attempt #1 Attempt #2 Attempt #3 Attempt...
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...
10. Stokes' Theorem and Surfac e Integrals of Vector Fields a. Stokes' Theorem: F-dr= b. Let S be th ky-plane. Draw a sketch of curve C in the xy-plane. et be the surface of the paraboloid z 4-x-y and Cis the trace of S in the c Let Fox.y.z) <2z, x, y>, Compute the curl (F) d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) F-dr Use Stokes' Theorem to compute , e. 10. Stokes' Theorem and Surfac...
Use (part A) line integral directly then use (part B) Stokes' Theorem 10. Let C be the triangle from (0, 0,0) to (2, 0, 0) to (0, 2, 1) to (0, 0, 0) which lies in the plane z 2 -Зугі + 4zj + 6x k, calculate | F . dr using Stokes's Theorem. If F(x, y, z) (b) 14 3 (c) 2 (d) 0 (e) None of these 10. Let C be the triangle from (0, 0,0) to (2,...
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y?». Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) e. Use Stokes' Theorem to computec F dr 10. Stokes' Theorem and Surface Integrals...
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y, Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)ーーーーーーーーーーーーー Compute N(u,v) e. Use Stokes' Theorem to compute Jc F dr 10. Stokes Theorem and Surface...
15.8 a. Use Stokes' Theorem to evaluate fF.dr where F(x,y,z) = (32-2y)i + (4x – 3y)j + (z +2y)k and C is the boundary of the triangle joining the points (1, 0, 0), (0, 1, 0), and (0, 0, 1). b. Find F.dr where F = 2zi - xj + 3y2k and S is the portion of the plane 3x + 3y + 2z = 6 in the first octant and C is its boundary.