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Let f(x, y, z) = ) = 9 (√x² − 4y² + 2²) x² + 16y² + 2², where g is some nonnegative function of one variable such that g(1) = 3. Let S be the surface defined by R(u, v) =(√1 +4v² cos u, v, √1 +4v² sin u u), where (u, v) € [0, 2π] × [0, 1]. Find the mass of a curved lamina in the shape of S if the density at each point (x, y, z) € S is given by f(x, y, z).

Let f(x, y, z) = ) = 9 (√x² − 4y² + 2²) x² + 16y² + 2², where g is some nonnegative function of one variable such that g(1) = 3. Let S be the surface defined by R(u, v) =(√1 +4v² cos u, v, √1 +4v² sin u u), where (u, v) € [0, 2π] × [0, 1]. Find the mass of a curved lamina in the shape of S if the density at each point (x, y, z) € S is given by f(x, y, z).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Let f(x, y, z) = 9 (√√x² − 4y² + 2² V x² + 16y² + 2², where g is some nonnegative function of one variable such that g(1) = 3. Let S be the surface defined by R(u, v) = (√√1 +4v² cos u, v, √1+ inu), √1 +4v² sin X where (u, v) [0, 2π] × [0, 1]. Find the mass of a curved lamina in the shape of S if the density at each point (x, y, z) ES is given by f(x, y, z).
Transcribed Image Text:Let f(x, y, z) = 9 (√√x² − 4y² + 2² V x² + 16y² + 2², where g is some nonnegative function of one variable such that g(1) = 3. Let S be the surface defined by R(u, v) = (√√1 +4v² cos u, v, √1+ inu), √1 +4v² sin X where (u, v) [0, 2π] × [0, 1]. Find the mass of a curved lamina in the shape of S if the density at each point (x, y, z) ES is given by f(x, y, z).
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