EXAM 2
MATH 22
Name:
____________________________
Winter 2001
Section: __________
You must
show all work clearly
to receive full credit.
(8) 1)
Find and sketch the domain of the function
.
f
x y
x
y
x
y
( ,
)
ln(
)
=
+
+


1
1
2
2
2
2
(10) 2)
Determine the largest set on which the function g is continuous. Give your reasoning.
g x y
xy
x
xy
y
( , )
=
+
+
2
2
0
if
if
( ,
)
( , )
( ,
)
( , )
x y
x y
≠
=
0 0
0 0
(6) 3)
Find
if
.
¶
¶
z
x
xyz
x
y
z
=
+
+
ln(
)
(8) 4)
Determine if there exists a function f with
and
f
x y
x
y
x
( , )
cos(
)
=
+
and whose second partial derivatives are continuous. Give
your
f
x y
x
y
y
( ,
)
sin(
)
=


p
2
reasoning.
(10) 5)
Is
differentiable at (2,2)?
If not, give your reasoning. If so, find the
f
x y
x
y
( ,
)
=
linearization L(x,y) of
f
at (2,2).
(8) 6)
For
,
show that
.
f
x y
xy
y
( ,
)
=
+
2
2
x
f
x
y
f
y
f
x y
¶
¶
¶
¶
+
=
2
( ,
)
7)
Given the surface
,
x
z
y
2
2
2
+
=
(8)
(a)
find the equation of the tangent plane to the surface at the point
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