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Chapter 14: Q. 44 (page 1120)
Find
Where S is the portion of the sphere with radius 2, centered at the origin, and that lies below the plane with equation , with n pointing outwards.
Ans:
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Find the integral of on the portion of the plane with the equation
with 2 ≤ x ≤ 7 and 1 ≤ z ≤ 2.
Give an example of a field with positive divergence at (1, 0, π).
Find the masses of the lamina:
The lamina occupies the region of the hyperboloid with equation that lies above and/or below the disk of radius 5 about the origin in the XY-plane, and the density function, ρ(x, y,z), is proportional to the distance from the origin.
Give a formula for a normal vector to the surface S determined by x = f(y, z), where f(y, z) is a function with continuous partial derivatives.
Find, where S is the portion of the surface determined bythat lies above the region in the xy-plane bounded by the x-axis and the lines with equations.
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