Stewart_Calc_7ET ch16sec05
MULTIPLE CHOICE
1. Find the correct identity, if f is a scalar field, F and G are vector fields.
a.
b.
c.
d.
None of these
2. Let
a.
9
b.
45
c.
18
d.
27
e.
None of these
3. Below is given the plot of a vector field F in the xy-plane. (The z-component of F is 0.) By
studying the plot, determine whether div F is positive, negative, or zero.
a.
cannot be determined
b.
positive
c.
negative
d.
zero
4. Find the divergence of the vector field F.
a.
b.
c.
d.
5. Find the curl of the vector field F.
a.
b.
c.
d.
6. Find the curl of the vector field.
a.
b.
c.
d.
e.
None of these
NUMERIC RESPONSE
1. Find the curl of the vector field.
2. Let
3. Find the curl of .
4. Find the curl of the vector field.
5. Find the divergence of the vector field.
6. Determine whether or not vector field is conservative. If it is conservative, find a function f
such that
7. Find the div F if .
8. Determine whether or not vector field is conservative. If it is conservative, find a function f
such that
9. Let
SHORT ANSWER
1. Find (a) the divergence and (b) the curl of the vector field F.
2. Let f be a scalar field. Determine whether the expression is meaningful. If so, state
whether the expression represents a scalar field or a vector field.
3. Let f be a scalar field. Determine whether the expression is meaningful. If so, state
whether the expression represents a scalar field or a vector field.
curl f
4. Let F be a vector field. Determine whether the expression is meaningful. If so, state whether
the expression represents a scalar field or a vector field.
5. Let F be a vector field. Determine whether the expression is meaningful. If so, state whether
the expression represents a scalar field or a vector field.
curl (div F)