|TIME: 3 HOURS|
|(5)||1.||Show is a conservative vector field and find a potential function for .|
||Find the volume of the solid bounded above by the cone
and below by
z = x2 + y2.
You need not evaluate any integrals for the questions on the remainder of the exam.
Set up an integral for the area of that part of
z = y2 - x2 that lies between the cylinders
x2 + y2
= 1 and
x2 + y2 = 4.
Let C be the closed curve consisting of the
arc of y = x2 from (0,0) to (1,1) and then the straight line
from (1,1) to (0,0).
||Using Green's Theorem, set this up as a double integral.
Set up the two integrals of Stokes Theorem
for the vector field
and the surface consisting of that part of
z = 1 - x2 - y2 that lies above the xy plane.
Set up the two integrals of the Divergence
Theorem for the vector field
and the unit ball
Find power series representations of the
following (either present the general term or at least 5 non-zero
||Find the radius of convergence for
||What is the sum of
Use power series to solve the
following differential equation.
Give at least 5 non-zero terms or state the general term.