Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.F = xyi + y2j - 2yzk ; D: the solid wedge cut from the first quadrant by the plane
and the parabolic cylinder x = 16 - 16y2
A.
B.
C.
D.
Answer: D
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Use the given transformation to evaluate the integral.
Rwhere R is the parallelepiped bounded by the planes
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A. 4095
B.
C. 1820
D. 455
Express the integrand as a sum of partial fractions and evaluate the integral.
A. tan-1
+ ln
-
+ C
B. tan-1
-
+
+ C
C. tan-1 -
-
+ C
D. tan-1
+
-
+ C
Complete the square to write the equation in the form +
= 1 or
+
= 1.Determine the center, foci, and vertices of the ellipse.9x2 + y2 - 72x + 135 = 0
A. (x - 3)2 + = 1
center: (3, 0); foci: (3, ), (3, -
); vertices:(3, 4), (3, -4)
B. + (y - 3)2 = 1
center: (3, 0); foci: (3, ), (3, -2
); vertices:(3, 4),
(3, -4)
C. + (y - 4)2 = 1
center: (4, 0); foci: (4, 2), (4, -2
); vertices:(4, 3), (4, -3)
D. (x - 4)2 + = 1
center: (4, 0); foci: (4, 2), (4, -2
); vertices:(4, 3), (4, -3)
Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.y = |17x|
A. x-axis only B. y-axis only C. Origin only D. x-axis, y-axis, origin