The average value of a function f(x, y, z) over a solid region E is defined to be 1 fave (E) . f (x, y, z) dv where V(E) is the volume of E. Find the average value of the function f(x, y, z) = x²z+y²z over the region enclosed by the paraboloid z = 1 - 2² - y² and the plane z = 0.
The average value of a function f(x, y, z) over a solid region E is defined to be 1 fave (E) . f (x, y, z) dv where V(E) is the volume of E. Find the average value of the function f(x, y, z) = x²z+y²z over the region enclosed by the paraboloid z = 1 - 2² - y² and the plane z = 0.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 40E: For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b...
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Transcribed Image Text:The average value of a function f(x, y, z) over a solid region
E is defined to be
1
(E) JJ, f ( x, y, z) dv
fave
where V(E) is the volume of E. Find the average value of the function
f(x, y, z) = x²z+ y²z over the region enclosed by the paraboloid z = 1 -
2² - y² and the plane z = 0.
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