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Question 5. Consider the vector field F= 2° + y* + 2*)} (z, v, 2). Using the component test, verify that F is conservative. (b) Find a potential function for F. (c) Let S be the quadric surface defined by (r- 1)2 + (y+1)2 + 2z2 = 18. Find the points q on S where the integral %3D F. dr (0,0,0) attain its maximal and minimal values.

Question 5. Consider the vector field F= 2° + y* + 2*)} (z, v, 2). Using the component test, verify that F is conservative. (b) Find a potential function for F. (c) Let S be the quadric surface defined by (r- 1)2 + (y+1)2 + 2z2 = 18. Find the points q on S where the integral %3D F. dr (0,0,0) attain its maximal and minimal values.

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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Question 5. Consider the vector field F = (2² + y? + z?)}(2, y, 2). (a) Using the component test, verify that F is conservative. (b) Find a potential function for F. (c) Let S be the quadric surface defined by (r - 1)² + (y + 1)² + 2z² = 18. Find the points q on S where the integral F. dr attain its maximal and minimal values. (Hint: Use theorems of vector calculus to reformulate this as a Lagrange multiplier problem.)
Transcribed Image Text:Question 5. Consider the vector field F = (2² + y? + z?)}(2, y, 2). (a) Using the component test, verify that F is conservative. (b) Find a potential function for F. (c) Let S be the quadric surface defined by (r - 1)² + (y + 1)² + 2z² = 18. Find the points q on S where the integral F. dr attain its maximal and minimal values. (Hint: Use theorems of vector calculus to reformulate this as a Lagrange multiplier problem.)
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