Calculus III
1. Find the curl of the vector field given by F(x, y, z) = ex sin y i - ex cos y j.
2. Find the divergence of the vector field F(x, y) = x2i + 2y2j.
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3. Find a potential function for the conservative vector field F(x, y) = 2xyi + (x2 – y)j.
4. Evaluate the line integral given below where C is the path r(t) = 4ti + 3tj, 0 ≤ t ≤ 1.
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5. Use the Fundamental Theorem of Line Integrals to evaluate the line integral
where C is the parabola y = 4 – x2 from (2, 0) to (0, 4).
xyds
C
ò
2xydx + ( x2
C
∫ + y2 )dy
2xydx+(x
2
C
ò
+y
2
)dy