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  3. consider f and c below. f(x, y, z) = 2xz +

Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j + x2 +...

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Question

Basic Math

Consider F and C below.

F(x, y, z) =

2xz + y2

i + 2xy j +

x2 + 6z2

k

C: x = t2,    y = t +2,    z = 3t − 1,    0 ≤ t≤ 1

(a) Find a function f such that F =∇f.

f(x, y, z) =

x2z+xy2+2z3+c

   

(b) Use part (a) to evaluate

  
C

∇f · dr along the given curve C.

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