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Stewart_Calc_7ET ch16sec07
MULTIPLE CHOICE
1. Suppose that where g is a function of one variable such that
.
Evaluate where S is the sphere
a.
b.
c.
d.
e.
None of these
2. Evaluate the surface integral.
S is the part of the plane that lies in the first octant.
a.
b.
c.
d.
e.
3. Evaluate the surface integral. Round your answer to four decimal places.
S is surface
a.
b.
c.
d.
e.
4. The temperature at the point in a substance with conductivity is
Find the rate of heat flow inward across the cylindrical
a.
b.
c.
d.
e.
5. Evaluate .
; S is the part of the plane in the first octant.
a.
0
b.
c.
d.
6. Evaluate .
; S is the part of the cone between the planes
and .
a.
b.
c.
d.
0
7. Evaluate .
327
35
59
2 139
42
; S is the part of the torus with vector representation
, , .
a.
0
b.
c.
d.
8. Find the mass of the surface S having the given mass density.
S is part of the plane in the first octant; the density at a point P on S is equal
to the square of the distance between P and the xy-plane.
a.
b.
c.
49
d.
20
9. Find the mass of the surface S having the given mass density.
S is the hemisphere , ; the density at a point P on S is equal to the
distance between P and the xy-plane.
a.
b.
c.
9
d.
10. Evaluate , that is, find the flux of F across S.
; S is the hemisphere ; n points upward.
a.
27
b.
162
c.
d.
162
11. Let S be the cube with vertices . Approximate by using a
Riemann sum as in Definition 1, taking the patches to be the squares that are the faces of
the cube and the points to be the centers of the squares.
a.
b.
c.
d.
e.
none of these
12. Evaluate the surface integral where S is the surface with parametric equations ,
.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Evaluate the surface integral for the given vector field F and the oriented surface
S. In other words, find the flux of F across S.
54
in the first octant,
with orientation toward the origin.
2. A fluid with density flows with velocity Find the rate of flow upward
through the paraboloid
3. Evaluate the surface integral. S is the part of the cylinder between the planes
and in the first octant.
4. Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone
if its density function is
5. Use Gauss's Law to find the charge contained in the solid hemisphere
, if the electric field is
6. Evaluate the surface integral for the given vector field F and the oriented surface
S. In other words, find the flux of F across S.
SHORT ANSWER
1. Evaluate , that is, find the flux of F across S.
; S is the part of the paraboloid between the planes z =
0 and z = 5; n points upward.
