Larson_Calculus_10e ch15sec01
MULTIPLE CHOICE
1. Sketch the vector field .
a.
d.
b.
e.
c.
2. Sketch several representative vectors in the vector field given by .
a.
d.
b.
e.
c.
3. Compute for the vector field given by .
a.
b.
c.
d.
e.
4. Find the gradient vector for the scalar function. (That is, find the conservative vector field for the
potential function.)
a.
b.
c.
d.
e.
5. Find the gradient vector for the scalar function. (That is, find the conservative vector field for the
potential function.)
a.
b.
c.
d.
e.
6. Find the conservative vector field for the potential function by finding its
gradient.
a.
b.
c.
d.
e.
7. Determine whether the vector field is conservative.
a.
conservative
b.
not conservative
8. Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
a.
conservative with potential function
b.
conservative with potential function
c.
conservative with potential function
d.
conservative with potential function
e.
not conservative
9. Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
a.
conservative with potential function
b.
conservative with potential function
c.
conservative with potential function
d.
conservative with potential function
e.
not conservative
10. Find the curl for the vector field at the given point.
a.
b.
c.
d.
e.
11. Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
a.
conservative with potential function
b.
conservative with potential function
c.
conservative with potential function
d.
conservative with potential function
e.
not conservative
12. Find the divergence of the vector field.
a.
b.
c.
d.
e.
13. Find the divergence of the vector field F given by .
a.
b.
c.
d.
e.
14. Find the divergence of the vector field at the given point.
a.
b.
c.
d.
e.
15. Find the divergence at for the vector field
a.
b.
c.
d.
e.
16. Find .
a.
b.
c.
d.
e.
17. Find .
a.
b.
c.
d.
e.
18. Find .
a.
b.
c.
d.
e.
19. Find for the vector field given by .
a.
b.
c.
d.
e.