Math22lO Quiz 6
(Sections 12.3-12.5)
Summer, 2012
7-17L0)a
Date
Name
Instructions:
appropriate,
Dylan Zwick
Please show all of your work as partial credit will be given where
and
there may be no credit given for problems where there is no work
All answers should be completely simplified, unless otherwise stated.
shown.
1. (15
points) Find the limit of
xy
urn
or state and explain why
(x,y)—(O,O) Jx 2 +y 2
ii
(o Y
it does not exist.
r/n
-
JiY1
1Y
r-o
_
IIPI’7
—
o
1co;i(fr1&
J’V31
1CO5,
(—7 C)
rcosOJ-I,’, Oo
Y—7()
2. (10
at
points)
Answer:
Find the equation of the tangent plane of 2
y+3xy atthe point
3
f(x,y)x
p=(2,—2) ?
(z,-
(-U
I (? (-?)
<3x’y 3
y
v (i,-L)
=
X+
xy?
<3(z)(-)k3(-
2
z)(-z)
-7,y--)
+ -Iz,-1-
tL-16\/ 7
/
Answer:
Jj
+
Use this to find the
3. (15 points) Find Vf given 2
—3xy+2y
f(x,y)=x
directional derivative of f at the point (—1,2) in the direction of the vector
2i—j
H
7
A
a
t,zI1
p
_tI
Vf:
KZ-3
Directional Derivative
L