Math22lO Quiz 5 (Sections 12.1, 12.2)
Name
Summer, 2012
Date
Dylan Zwick
7/l0i2
/
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. Let
(a) Sketch the surface defined by the above equation:
(b) Sketch the level curves for
f(x,y)=k where
I
(c) What the the domain? Domain:
All
JR
k=0,1,2,3
2. Find the slope of the tangent to the curve of intersection of the surface
z=4x2+3xy2_2xy+sin(x)+3y2 and the plane
x0
at the point
(0,2,12)
y_/
.
(o
t
1
)
oft)- (o) (1
slope
3. Fortheabovesurface
(a)
LL1
=
z=
+
2
_
2xy+sin(-.x)+
3xy
4x
3y2 calculate:
öz
--—
ox
yLZy
oq)
Answer:
82
(b)
z
oy
Answer:
6
Answer:
1
z
OxOy
02
(c)