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Problem 2. Let F be the vector field (xe² + cos(x), -ye², z sin(x)), and S the paraboloid z = 1- x2 – y?, z 2 0 with upward pointing normal vector. 1. Calculate the divergence of F, V ·F. 2. Calculate the flux of F though S, || 1 . ds.

Problem 2. Let F be the vector field (xe² + cos(x), -ye², z sin(x)), and S the paraboloid z = 1- x2 – y?, z 2 0 with upward pointing normal vector. 1. Calculate the divergence of F, V ·F. 2. Calculate the flux of F though S, || 1 . ds.

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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Need help with part 2. Please explain each step and neatly type up. Thank you :)

Problem 2. Let F be the vector field (xe² + cos(x), -ye², z sin(x)), and S the paraboloid z = 1- x2 – y?, z 2 0 with upward pointing normal vector. 1. Calculate the divergence of F, V · F. 2. Calculate the flux of F though S, F. ds. F. dS.
Transcribed Image Text:Problem 2. Let F be the vector field (xe² + cos(x), -ye², z sin(x)), and S the paraboloid z = 1- x2 – y?, z 2 0 with upward pointing normal vector. 1. Calculate the divergence of F, V · F. 2. Calculate the flux of F though S, F. ds. F. dS.
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