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 33PS
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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Figure 1.
Chapter 13 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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- az. Suppose F = (2xz + 3y²) a, + (4yz²) a;. (a) Calculate S[F·dS, where S is the shaded surface in Figure 1. (c) Based on your results for parts (a) and (b), what named theorem do you think is being satisfied here, if any? (b) Calculate SF· dl, where C is the A → B → C → D → A closed path in Figure 1. az C C (0,1,1) D (0,0,0) (A ay В ax Figure 1: Figure for Problem 1.arrow_forward5. If S is the surface x6+y6 +26 = 1 and F is some me vectorfield, calculate ff V × F.d.S.arrow_forwardxy- plañé. 2. Let vector field F=(xz,-y,z) and surface, S is a cylinder x + y = 4 for 3szs0 with the outward pointing normal vector. Use Stokes' Theorem to evaluate curl F dS . 3. Verify Stokes' Theorem for the vector field F =2zi +3xj+5yk, taking S to be a portion of thearrow_forward
- 03. a. If F = (y² + z² − x²)i + (z² + x² − y²)j + (x² + y² − z²)k, then evaluate, SS V × F · n dA integrated over the portion of the surface x² + y² − 4x + 2z = 0 above the plane z = 0 and verify the Stroke's Theorem. n is the unit vector normal to the surface.arrow_forward- y², Consider the vector field F = (2x, 3y, 4z) and the surface z = 4-2² Write down the line integral and the surface integral that Stokes' Theorem tells us are equal vector field and surface. Evaluate both. Hint: The surface integral requires very little work. You do not even need to parameterize the surface. 2 ≥ 0. for thisarrow_forwardP.nilarrow_forward
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