|APRIL 1996||TIME: 3 HOURS|
where D is the region between the circles and
||(5)||4.||Find the volume of the solid cut from the sphere
by the cone . [Here ()
represent the usual spherical coordinates.]
||(5)||5.||Find the area of the region enclosed by . [Here represent the usual polar
. Show that is
conservative and find a function such
|The solution to the following problems is an interated integral.
DO NOT evaluate the integral.|
is the unit circle oriented counterclockwise.
||(a)||Set this up as a single integral.
||(b)||Use Greens Theorem to set this up as a double
||(5)||8.||Let be the unit circle with up
ward orientation, and C be the boundary
of S. Use Stokes theorem to write as a double integral.
||(5)||9.||Set up an iterated integral for the
work done by the force field
in moving a particle along the line segment from
||(5)||10.||Use the divergence theorem to write
as a triple integral where
and S is the surface of
the cylinder .
||(5)||11.||Set up an integral for the volume of the solid
bounded by and the planes z = 0
and x + z = 1.
||(5)||12.||Set up an integral for the surface area of that part of
the cylinder that lies inside the cylinder .|
|(8)||13.||Explain why the
following series converge or diverge:
||(a)||(b)||(c)||(d)||(9)||14.||Find at least 5 non-zero terms of the Maclaurin series
||(4)||15.||Find the radius of convergence for
||(9)||16.||Use power series to solve
||(Find at least 4 non-zero terms.)