Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
6th Edition
ISBN: 9781524908102
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.7, Problem 32PS
To determine
To calculate: The value of the surface integral
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2. Let S denote the piece of parabolic surface x2 + y? = z, 0 < z < 4. For the vector
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13
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Figure 1.
3.1. Consider the vector field F(x, y, z) = (2yz, y sin z, 1+ cos z).
(a) Find a vector field G whose curl is F.
(b) Let S be the half-ellipsoid 4x² + 4y² + z² = 4, z ≥ 0, oriented by the upward normal.
Use Stokes's theorem to find ffs F. ds.
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Chapter 13 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
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- 2. Let vector field F=(xz, -y,z) and surface, S is a cylinder x² + y² =4 for 3sz≤0 with the outward pointing normal vector. Use Stokes' Theorem to evaluate curl F.ds.arrow_forwardPlease help wth the following questions. They are in the photo.arrow_forwardIf F(x, y, z)= xz i + xyz j - y 2 k find curl Farrow_forward
- 6. Suppose the surface S is given by the part of the paraboloid z = x² + y² that lies inside the cylinder x² + y² = 1, with unit normal vector pointing upward. Using Stokes' Theorem, evaluate the integral for the vector field JJ S F(x, y, z) = (y²z)i + (xz)j + (x²y²) k. (V x F).dSarrow_forwardSolve first 2arrow_forward
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