Larson_Calculus_10e ch15sec06
MULTIPLE CHOICE
1. Evaluate , where
.
a.
b.
c.
d.
e.
2. Evaluate , where .
a.
b.
c.
d.
e.
3. Evaluate , where S is , first octant.
a.
b.
c.
d.
e.
4. Use a computer algebra system to evaluate where S is . Round
your answer to two decimal places.
a.
124.82
b.
1.07
c.
62.41
d.
141.01
e.
64.00
5. Use a computer algebra system to evaluate where S is
. Round your answer to two decimal places.
a.
–475.02
b.
–496.00
c.
–203.00
d.
–971.38
e.
6. Find the mass of the surface lamina S of density .
a.
b.
c.
d.
e.
7. Evaluate , where
.
a.
b.
c.
d.
e.
8. Evaluate , where and S is given by
.
a.
8
b.
32
c.
16
d.
96
e.
512
9. Evaluate , where and S is given by .
a.
10,000
b.
c.
d.
e.
10. Evaluate , where and S is given by
.
a.
b.
c.
d.
e.
11. Evaluate , where
.
a.
b.
c.
d.
e.
12. Find the flux of through S, , where is the upward unit normal vector to S.
, first octant
a.
b.
c.
d.
e.
13. Find the flux of through S, , where is the upward unit normal vector to S.
a.
b.
c.
d.
e.
14. Find the flux of through where N is the
upward unit normal vector to S.
a.
8
b.
11
c.
1
d.
e.
4
15. Find the flux of over the closed surface (let be the outward unit normal vector of the surface).
S: cube bounded by
a.
200
b.
800
c.
400
d.
1,000
e.
600
16. Let be an electrostatic field. Use Gauss’s Law to find the total charge enclosed by the
closed surface consisting of the hemisphere and its circular base in the xy-plane.
a.
b.
c.
d.
e.
17. Find for the lamina with uniform density of 1. Use a computer algebra
system to verify your result.
a.
b.
c.
d.
e.
18. Let S be the surface oriented upwards. Use a computer algebra system to find
the rate of mass flow of a fluid of density through S if the velocity field is given by
.
a.
b.
c.
d.
e.