Consider F and C below. F(x, y) = (1 + xy)exy i + x²exy j C: r(t) = cos(t) + 3 sin(t)j, osts (a) Find a function f such that F = Vf. f(x, y) = 플 (b) Use part (a) to evaluate F. dr along the given curve C.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 44E
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Consider F and C below.
F(x, y) = (1 + xy)exy i + x²exyj
Π
C: r(t) = cos(t) + 3 sin(t)j, 0 ≤ts 1
i
(a) Find a function f such that F = Vf.
f(x, y) =
(b) Use part (a) to evaluate
F. dr along the given curve C.
Transcribed Image Text:Consider F and C below. F(x, y) = (1 + xy)exy i + x²exyj Π C: r(t) = cos(t) + 3 sin(t)j, 0 ≤ts 1 i (a) Find a function f such that F = Vf. f(x, y) = (b) Use part (a) to evaluate F. dr along the given curve C.
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