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Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface bounding E. (a) Find the surface area of S. x² + y² ≥ 1, z ≥ 0,

Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface bounding E. (a) Find the surface area of S. x² + y² ≥ 1, z ≥ 0,

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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Consider the solid E determined by the inequalities x² + y² + z ≤ 4, and let S denote the surface bounding E. (a) Find the surface area of S. (b) What is the outward flux of the vector field F = (y, z², 5z + ln(x² + y²)) across S? (c) What about the outward flux of curl(F) across the part of S where x² + y² + z = 4? x² + y² ≥ 1, z ≥ 0,
Transcribed Image Text:Consider the solid E determined by the inequalities x² + y² + z ≤ 4, and let S denote the surface bounding E. (a) Find the surface area of S. (b) What is the outward flux of the vector field F = (y, z², 5z + ln(x² + y²)) across S? (c) What about the outward flux of curl(F) across the part of S where x² + y² + z = 4? x² + y² ≥ 1, z ≥ 0,
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need help with part c please

Consider the solid E determined by the inequalities x² + y² + z ≤ 4, and let S denote the surface bounding E. (a) Find the surface area of S. (b) What is the outward flux of the vector field F = (y, z², 5z + ln(x² + y²)) across S? (c) What about the outward flux of curl(F) across the part of S where x² + y² + z = 4? x² + y² ≥ 1, z ≥ 0,
Transcribed Image Text:Consider the solid E determined by the inequalities x² + y² + z ≤ 4, and let S denote the surface bounding E. (a) Find the surface area of S. (b) What is the outward flux of the vector field F = (y, z², 5z + ln(x² + y²)) across S? (c) What about the outward flux of curl(F) across the part of S where x² + y² + z = 4? x² + y² ≥ 1, z ≥ 0,
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