Use the Divergence Theorem to calculate the surface integral S F
· dS; that is, calculate the flux of F across S. F(x, y, z) = x4i −
x3z2j + 4xy2zk, S is the surface of the solid bounded by the
cylinder x2 + y2 = 1 and the planes z = x + 8 and z = 0
Calculate the integral of the function f (x, y, z) = xyz on the
region bounded by the z = 3 plane from the bottom, z = x ^ 2 + y ^
2 + 4 paraboloid from the side, x ^ 2 + y ^ 2 = 1 from the top.
Determine how many times the innermost loop will be iterated
when the algorithm segment is implemented and run. (Assume that
m and n
are positive integers.)
for j := 1 to m
for k := 1 to n
[Statements in
body of inner loop.
None contain
branching statements that
lead outside
the loop.]
next k
next j