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11. Integrate f (x, y, z) = r (x²+ y2) dv over the cylindrical solid region bounded by z=0 and z= 4-/x2 + y?, 0< 0 >2n.

11. Integrate f (x, y, z) = r (x²+ y2) dv over the cylindrical solid region bounded by z=0 and z= 4-/x2 + y?, 0< 0 >2n.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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11. Integrate f (x, y, z) = r2 (x²+ y²) dv over the cylindrical solid region bounded by z=0 and z= 4-/x2 + y2, 0< e >2n. 12. Find the divergence and curl of the vector A" = xy i -2yj+4xz? k" at point P (1,2,1). 13. If A" = 31-2j+4k" and B"=2i-4j"+8k* then find A" x B", A". B" and the angle between the two vectors. 14. Prove that the following function satisfies Laplace equation and find its harmonic conjugate U= y3-3x?y
Transcribed Image Text:11. Integrate f (x, y, z) = r2 (x²+ y²) dv over the cylindrical solid region bounded by z=0 and z= 4-/x2 + y2, 0< e >2n. 12. Find the divergence and curl of the vector A" = xy i -2yj+4xz? k" at point P (1,2,1). 13. If A" = 31-2j+4k" and B"=2i-4j"+8k* then find A" x B", A". B" and the angle between the two vectors. 14. Prove that the following function satisfies Laplace equation and find its harmonic conjugate U= y3-3x?y
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