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(a) Show that the volume of the solid in R³ that lies below the surface z = f(x, y) and above the region D is equal to the volume of a cylinder of radius R and height z.

(a) Show that the volume of the solid in R³ that lies below the surface z = f(x, y) and above the region D is equal to the volume of a cylinder of radius R and height z.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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Please solve 2(a)

Q2. The average value z of z = f(x,y) on a subset D C R² is defined to be 1 // f(x, y) dA z = area(D) (provided the quantities on the RHS are well-defined and finite). {(x, y): x² + y² < R?}, and let f be a In what follows let R> 0 be a fixed constant, let D continuous function that is defined on D and satisfies f(x, y) > 0 for all (x, y) E D.
Transcribed Image Text:Q2. The average value z of z = f(x,y) on a subset D C R² is defined to be 1 // f(x, y) dA z = area(D) (provided the quantities on the RHS are well-defined and finite). {(x, y): x² + y² < R?}, and let f be a In what follows let R> 0 be a fixed constant, let D continuous function that is defined on D and satisfies f(x, y) > 0 for all (x, y) E D.
(a) Show that the volume of the solid in R³ that lies below the surface z = f(x, y) and above the region D is equal to the volume of a cylinder of radius R and height z.
Transcribed Image Text:(a) Show that the volume of the solid in R³ that lies below the surface z = f(x, y) and above the region D is equal to the volume of a cylinder of radius R and height z.
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