Math22lO Quiz 11 (Sections 13.8, 14.1)
Name
1<E
Summer, 2012
\/
Date
Dylan Zwick
73 Zo/
7
Instructions: Please show all of your work as partial credit will be given where
appropriate, and there may be no credit given for problems where there is no
work shown. All answers should be completely simplified, unless otherwise
stated.
1. (18 points) Calculate the volume of the solid bounded by the paraboloid
+y and the plane z=4
z=x
2
I i f
()
3
r
-
)d
C)
rZ
HL
Jo
/1
f
70
Zn
L1
Answer:
2. (14 points) Calculate dlv F and curl F for the vector field
F(x, y, z)excos(y)i+exsin(y) j+z k
F
oSy
(cx
±
coJY
divF:
curl F:
5ii
1<
\
If f(x,y,z) is a scalar function and F(x,y,z) is a vector field,
which of the following make sense (circle one):
3. (2 points each)
a)
VV(f)
Makes sense.
Does not make sense.
b) div(grad(f))
Makes sense.
c) grad(div(F))
Makes sense.
Does not make sense.
Makes sense.
Does not make sense.
d)
VxV(f)
‘
Does not make sense.