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SConsider the vector field F (x, y, z) = (z+ y) i+ (2z + x)j+(2y+x) k. a) Find a function f such that F = Vƒ and f(0,0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0,0) to (1, 1, 1). Use part a) to compute the line integral F- dr.

SConsider the vector field F (x, y, z) = (z+ y) i+ (2z + x)j+(2y+x) k. a) Find a function f such that F = Vƒ and f(0,0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0,0) to (1, 1, 1). Use part a) to compute the line integral F- dr.

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 vector field ?(?,?,?)=(?+?)?+(2?+?)?+(2?+?)? F ( x , y , z ) = ( z + y ) i + ( 2 z + x ) j + ( 2 y + x ) k . a) Find a function ? f such that ?=∇? F = ∇ f and ?(0,0,0)=0 f ( 0 , 0 , 0 ) = 0 . ?(?,?,?)= f ( x , y , z ) = b) Suppose C is any curve from (0,0,0) ( 0 , 0 , 0 ) to (1,1,1). ( 1 , 1 , 1 ) . Use part a) to compute the line integral ∫??⋅?? ∫ C F ⋅ d r .

Consider the vector field F (x, y, z) = (z+ y)i+(2z + x)j+(2y+x) k. a) Find a function f such that F Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0,0) to (1, 1, 1). Use part a) to compute the line integral F - dr.
Transcribed Image Text:Consider the vector field F (x, y, z) = (z+ y)i+(2z + x)j+(2y+x) k. a) Find a function f such that F Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0,0) to (1, 1, 1). Use part a) to compute the line integral F - dr.
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