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(28 points) Define T: [0,1] × [−,0] → R3 by T(y, 0) = (cos 0, y, sin 0). Let S be the half-cylinder surface traced out by T. (a) (4 points) Calculate the normal field for S determined by T. (b) (8 points) The boundary of S, i.e. Os, consists of two semi-circles when y = 0 and y = 1, along with two line segments that are parallel to the y-axis when 0 = 0 and when -π. Parametrize as. (c) (4 points) Let F(x, y, z) = (-yz, g(y), -xy) where g is a differentiable function of y only. Calculate the curl V x F.

(28 points) Define T: [0,1] × [−,0] → R3 by T(y, 0) = (cos 0, y, sin 0). Let S be the half-cylinder surface traced out by T. (a) (4 points) Calculate the normal field for S determined by T. (b) (8 points) The boundary of S, i.e. Os, consists of two semi-circles when y = 0 and y = 1, along with two line segments that are parallel to the y-axis when 0 = 0 and when -π. Parametrize as. (c) (4 points) Let F(x, y, z) = (-yz, g(y), -xy) where g is a differentiable function of y only. Calculate the curl V x F.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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(28 points) Define T: [0,1] × [−,0] → R3 by T(y, 0) = (cos 0, y, sin 0). Let S be the half-cylinder surface traced out by T. (a) (4 points) Calculate the normal field for S determined by T.
Transcribed Image Text:(28 points) Define T: [0,1] × [−,0] → R3 by T(y, 0) = (cos 0, y, sin 0). Let S be the half-cylinder surface traced out by T. (a) (4 points) Calculate the normal field for S determined by T.
(b) (8 points) The boundary of S, i.e. Os, consists of two semi-circles when y = 0 and y = 1, along with two line segments that are parallel to the y-axis when 0 = 0 and when -π. Parametrize as. (c) (4 points) Let F(x, y, z) = (-yz, g(y), -xy) where g is a differentiable function of y only. Calculate the curl V x F.
Transcribed Image Text:(b) (8 points) The boundary of S, i.e. Os, consists of two semi-circles when y = 0 and y = 1, along with two line segments that are parallel to the y-axis when 0 = 0 and when -π. Parametrize as. (c) (4 points) Let F(x, y, z) = (-yz, g(y), -xy) where g is a differentiable function of y only. Calculate the curl V x F.
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