Use Stokes’ Theorem to evaluate
Trending nowThis is a popular solution!
Chapter 16 Solutions
CALCULUS FULL TEXT W/ACCESS >BI<
- please help mearrow_forwardLet F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F - (b) What does your answer to part (a) tell you about SF. dr where C' is the circle (x − 15)² + (y – 10)² = 1 in the xy-plane, oriented clockwise? ScF. dr = 0 (c) If C is any closed curve, what can you say about ScF. dr? SoF. dr = 0 (d) Now let C be the half circle - (x − 15)² + (y − 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. -0 Lc F. dr =arrow_forward3. Let F and G be vector ficlds with differentiable components. Express curl (F x G) in term of div and dot products.arrow_forward
- Let F = Jo Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (10,0,0), (0,10,0), and (0,0,10), oriented counterclockwise as viewed from above.arrow_forwardLet us verify Stokes' theorem using the vector field F = (x 2 - y)i + 4zj + x 2k, where the closed contour consists of the x and y coordinate axes and that portion of the circle 2 + y 2 = a 2 that lies in the first quadrant with z = 1arrow_forwardPlease solve the screenshot (handwritten preferred) and explain your work, thanks!arrow_forward
- Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ğ(1, Y, 2) = (2r, y,0) and D is any closed curve.arrow_forward> Let F =< x²e³², xez, z²exy :// curl F. dS, where S Use Stokes' Theorem to evaluate S is the hemisphere x² + y² + z² = 1, z ≥ 0, oriented upwardsarrow_forwardLet F =. Compute the flux of curl(F) through the surface z = 1- x² - y² for x² + y² ≤ 11 oriented with an upward-pointing normal. Flux = help (fractions) (Use symbolic notation and fractions where needed.) Hint: Stokes' Theorem shows a direct computation can be done in an alternative fashion.arrow_forward
- Solve: If A = i sin 2t + je³t + k(t³ – 4t) Find when t = 1. dt If F = x²yzi + xyz²j + y²zk determine curl F at the point (2, 1, 1).arrow_forwardUse Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = tan-1(x²yz²)i + x?yj + x²z²k, S is the cone x = V y? + z?, 0 < x< 4, oriented in the direction of the positive x-axis.arrow_forwardVerify the Stokes' Theorem in evaluating F.dr if F(x, y, z) = z² i + 2xj-y³k, where C is the circle x² + y² = 1 in xy-plane with the counterclockwise orientation looking down the positive z-axis.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage