4) a) Find a potential function f (#, y, z) with Vf = F(r, y, 2) = yz? 7 + (xz² + 2z) + (2.ryz + 2y) k b) Use the potential function to evaluate Se FodT = fc yz?dx+ (xz? +22)dy + (2aryz+ 2g)dz, where C is any path from (2, 2, 3) to (1,0, 2). %3D c) What is the value of feyz?dx + (rz2 + 2z)dy + (2ryz + 2y)dz if C is the circle : r2 + y? = 16; z 5; traversed counterclockwise ?
4) a) Find a potential function f (#, y, z) with Vf = F(r, y, 2) = yz? 7 + (xz² + 2z) + (2.ryz + 2y) k b) Use the potential function to evaluate Se FodT = fc yz?dx+ (xz? +22)dy + (2aryz+ 2g)dz, where C is any path from (2, 2, 3) to (1,0, 2). %3D c) What is the value of feyz?dx + (rz2 + 2z)dy + (2ryz + 2y)dz if C is the circle : r2 + y? = 16; z 5; traversed counterclockwise ?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:4)
a) Find a potential function f (*, y, z) with
Vf = F(r, y, 2) = yz² i + (xz² + 2z)5 + (2ryz + 2y) k
b) Use the potential function to evaluate
le FodT = fc yz?dx + (xz2 +22)dy + (2aryz+2g)dz, where C is any path
from (2,2, 3) to (1,0, 2).
%3D
c) What is the value of feyz?dr + (rz2 + 2z)dy + (2ryz + 2y)dz if C is the
circle : r2 + y? = 16; z = 5; traversed counterclockwise ?
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