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Chapter 14: Q. 50 (page 1120)
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.
Ans:
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Give a formula for a normal vector to the surface S determined by y = g(x,z), where g(x,z) is a function with continuous partial derivatives.
Find the flux of the given vector field through a permeable membrane described by surface S.
, where S is the paraboloid with equation role="math" localid="1650299986090" that lies above the annulus determined by in the XY-plane.
If curl is constantly equal to on a smooth surface with a smooth boundary curve , then Stokes’ Theorem can reduce the integral for the surface area to a line integral. State this integral.
S is the portion of the saddle surface determined by z = x2 − y2 that lies above and/or below the annulus in the xy-plane determined by the circles with radii
and centered at the origin.
Let Rbe a simply connected region in the xy-plane. Show that the portion of the paraboloid with equation determined by R has the same area as the portion of the saddle with equation determined by R.
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