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Use Stokes's Theorem to evaluate F . In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + 3zj + xk C: triangle with...
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9. Use Stokes's Theorem to evaluate
F . dr
. In this case, C is oriented counterclockwise as
viewed from above.
F(x, y, z) = 2yi + 3zj + xk
C: triangle with vertices (3, 0, 0), (0, 3, 0), (0, 0, 3)
10. (a) Show that F (x , y ) = (3 x2 y2 , 2 x3 y - 4) is a conservative vector field and then (b)
find a potential function. (c) Evaluate
W = [ F(x, y) . dr
where Cruns fre (1, 2) to (-1, 1)
i. Find the volume of the parallelepiped with three adjacent edges formed by
(2, 1, 0), (-1, 2, 0), and (1, 1, 2).
ii. Using the definition of the limit of a function of two variables, show that
lim
(x,y)-(1,-3)
y = -3

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Subject: Calculus, Math

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