1. Let f(x, y, z) = 9 (√x² + y² + z2²) 7 where g is some nonnegative function of one variable such that g(2) = 1/4. Suppose S₁ is the surface parametrized by R(0, 6) = 2 cos 0 sin oi + 2 sin 0 sin øj + 2 cos ok, where (0, 6) = [0, 2π] × [0, π]. a. Find Rex Rø, for all (0, 6) = [0, 2π] × [0, π]. b. If the density at each point (x, y, z) € S₁ is given by f(x, y, z), use a surface integral to compute for the mass of S₁.
1. Let f(x, y, z) = 9 (√x² + y² + z2²) 7 where g is some nonnegative function of one variable such that g(2) = 1/4. Suppose S₁ is the surface parametrized by R(0, 6) = 2 cos 0 sin oi + 2 sin 0 sin øj + 2 cos ok, where (0, 6) = [0, 2π] × [0, π]. a. Find Rex Rø, for all (0, 6) = [0, 2π] × [0, π]. b. If the density at each point (x, y, z) € S₁ is given by f(x, y, z), use a surface integral to compute for the mass of S₁.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Let f(x,y,z) = g(sqrt(x2 + y2 + z2).
![1. Let f(x, y, z) = 9 (√x² + y² + z2²)
7
where g is some nonnegative function of one variable
such that g(2) = 1/4. Suppose S₁ is the surface parametrized by
R(0, 6) = 2 cos 0 sin oi + 2 sin 0 sin øj + 2 cos ok,
where (0, 6) = [0, 2π] × [0, π].
a. Find Rex Rø, for all (0, 6) = [0, 2π] × [0, π].
b. If the density at each point (x, y, z) € S₁ is given by f(x, y, z), use a surface integral to
compute for the mass of S₁.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb4e7eaf-fc8a-4a28-807c-7b9f451fe6e4%2F4c9c8880-c61a-49ec-babc-1366e7170f5f%2Flhgso0t_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let f(x, y, z) = 9 (√x² + y² + z2²)
7
where g is some nonnegative function of one variable
such that g(2) = 1/4. Suppose S₁ is the surface parametrized by
R(0, 6) = 2 cos 0 sin oi + 2 sin 0 sin øj + 2 cos ok,
where (0, 6) = [0, 2π] × [0, π].
a. Find Rex Rø, for all (0, 6) = [0, 2π] × [0, π].
b. If the density at each point (x, y, z) € S₁ is given by f(x, y, z), use a surface integral to
compute for the mass of S₁.
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