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mmer 2019 3. Evaluate: M y2 dV where E the solid hemisphere x2 + y2 +z2 9 and y 2 0 indrnse)
mmer 2019 3. Evaluate: M y2 dV where E the solid hemisphere x2 + y2 +z2 9 and y 2 0 indrnse)
Evaluate the integral, where E is the region that lies inside the cylinder x2 + y2 = 4 and between the planes z = -1 and z = 0. Use cylindrical coordinates. SSSE V.x2 + y2 DV =
Evaluate the triple integral.
3z
dV, where E is bounded by the cylinder
y2 + z2 = 9 and the planes
x = 0, y = 3x, and z = 0 in the
first octant
E
5. Evaluate /// (y +z) dV where E is bounded by x = 0, y = 0, x2 + y2 + z2 = 1, and x2 + y2 + 2?" = 9. Use spherical coordinates. Answer must be exact values.
Use spherical coordinates.
Evaluate
(4 − x2 − y2) dV, where H is
the solid hemisphere x2 + y2 + z2
≤ 16, z ≥ 0.
H
Compute the volume SSSx 1 dV where X is the solid defined by x2 + y2 < 4,0 Sz<10., A) 20 B) 407 C) 201 D) 801 ОА ОС OD OB Question 20 What is the absolute value of the Jacobian of : x = uv, y = u2 + v2 at the input point (u, v) = (2, 3)?
Evaluate Sed = 25 and E 1 dV, where E lines between the spheres x2 + y2 + x2 x2 + y2 + 22 = 36 in the first octant. x² + y2 + z2
Use cylindrical coordinates. Evaluate SIS x2 + y2 dv, where E is the region that lies inside the cylinder x2 + y2 = 4 and between the planes z = 3 and z = 12. x
Evaluate SSS, (x² + y2 + z)ele?+y't??)? DV, where B is the unit ball: B={(x,y,z)/x² + y2 +2+ <1}
Problem 8. (1 point) If z2 = x2 + y2 with z > 0, dx/dt 4, and dyldt = 5, find dzldt when x = 12 and y = 35. dz Answer: dt =