Stewart_Calc_7ET ch16sec03
MULTIPLE CHOICE
1. Determine whether F is conservative. If so, find a function f such that .
a.
b.
not conservative
c.
d.
2. Determine whether F is conservative. If so, find a function f such that .
a.
b.
not conservative
c.
d.
3. Show that F is conservative and find a function f such that , and use this result to
evaluate , where C is any path from to .
; and
a.
b.
c.
d.
4. Evaluate for the vector field F and the path C. (Hint: Show that F is conservative,
and pick a simpler path.)
C:
a.
b.
54
c.
0
d.
19
5. Show that F is conservative, and find a function f such that , and use the result to
evaluate , where C is any curve from to .
; and
a.
–109
b.
45
c.
–62
d.
–44
6. Find the value of the constant c such that the vector field
is the curl of some vector field F.
a.
–7
b.
0
c.
12
d.
3
7. Show that F is conservative and find a function f such that , and use this result to
evaluate , where C is any path from to .
; and
a.
b.
c.
d.
8. Show that F is conservative, and find a function f such that , and use the result to
evaluate , where C is any curve from to .
; and
a.
–113
b.
–24
c.
–131
d.
–178
9. Let where .
Which of the following equations does the line segment from to satisy?
a.
b.
c.
none of these
NUMERIC RESPONSE
1. Determine whether or not F is a conservative vector field. If it is, find a function f such
that
.
2. Determine whether or not F is a conservative vector field. If it is, find a function f such
that
3. Find a function f such that , and use it to evaluate along the given curve
C.
4. Determine whether or not F is a conservative vector field. If it is, find a function f such
that
5. Determine whether or not F is a conservative vector field. If it is, find a function f such
that
6. Determine whether or not vector field is conservative. If it is conservative, find a function f
such that
7. Find a function f such that , and use it to evaluate along the given curve
C.
8. Find a function f such that and use it to evaluate along the given curve
C.
C is the upper semicircle that starts at (1, 2) and ends at (5, 2).
9. Suppose that F is an inverse square force field, that is,
where Find the work done by F in moving an object from a point along a
path to a point in terms of the distances and from these points to the origin.
SHORT ANSWER
1. Determine whether F is conservative. If so, find a function f such that .
2. Determine whether F is conservative. If so, find a function f such that .