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1. Consider the following three domains in the space: {(x,y,z) E R³:1 ≤|x+y+z<4}, {(x,y,z) € R³ : 2 ≤ x² + y² + z² ≤ 9, x ≤0, y ≥ 0 och z ≤ 0}, {(x,y,z) € R³ : 1 ≤ x² + y² ≤ 3, x ≥ 0, y ≤0 och 0 ≤ z ≤ 4}. a) Snerify the boundary points of D₁ and is D₁ closed, open, and/or bounded? (Ch. 10.1) D₁ D2 D3 = = b) Describe D₂ in spherical coordinates. (Ch. 10.5, 10.6) c) Describe D3 in cylindrical coordinates. (Ch. 10.5, 10.6)

1. Consider the following three domains in the space: {(x,y,z) E R³:1 ≤|x+y+z<4}, {(x,y,z) € R³ : 2 ≤ x² + y² + z² ≤ 9, x ≤0, y ≥ 0 och z ≤ 0}, {(x,y,z) € R³ : 1 ≤ x² + y² ≤ 3, x ≥ 0, y ≤0 och 0 ≤ z ≤ 4}. a) Snerify the boundary points of D₁ and is D₁ closed, open, and/or bounded? (Ch. 10.1) D₁ D2 D3 = = b) Describe D₂ in spherical coordinates. (Ch. 10.5, 10.6) c) Describe D3 in cylindrical coordinates. (Ch. 10.5, 10.6)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the following three domains in the space: {(x,y,z) € R³ : 1 ≤ x+y+z<4}, {(x,y,z) € R³ : 2 ≤ x² + y² + z² ≤ 9, x ≤0, y ≥ 0 och z ≤ 0}, {(x,y,z) € R³ : 1 ≤ x² + y² ≤ 3, x>0, y ≤0 och 0 ≤ ≤ 4}. a) Snerify the boundary points of D₁ and is D₁ closed, open, and/or bounded? (Ch. 10.1) D₁ D2 D3 = = b) Describe D₂ in spherical coordinates. (Ch. 10.5, 10.6) c) Describe D3 in cylindrical coordinates. (Ch. 10.5, 10.6)
Transcribed Image Text:1. Consider the following three domains in the space: {(x,y,z) € R³ : 1 ≤ x+y+z<4}, {(x,y,z) € R³ : 2 ≤ x² + y² + z² ≤ 9, x ≤0, y ≥ 0 och z ≤ 0}, {(x,y,z) € R³ : 1 ≤ x² + y² ≤ 3, x>0, y ≤0 och 0 ≤ ≤ 4}. a) Snerify the boundary points of D₁ and is D₁ closed, open, and/or bounded? (Ch. 10.1) D₁ D2 D3 = = b) Describe D₂ in spherical coordinates. (Ch. 10.5, 10.6) c) Describe D3 in cylindrical coordinates. (Ch. 10.5, 10.6)
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