MATH 241: TEST 2
Name
Instructions and Point Values:
Put your name in the space provided above. Work
each problem below and show ALL of your work. You do not need to simplify your answers.
Do NOT use a calculator.
Problem (1) is worth 12 points.
Problem (2) is worth 14 points.
Problem (3) is worth 14 points.
Problem (4) is worth 14 points.
Problem (5) is worth 14 points.
Problem (6) is worth 16 points.
Problem (7) is worth 16 points.
(1) Let
f
(
x; y
)=
x
3
y
x
4
+
y
4
:
Does lim
(
x;y
)
!
(0
;
0)
f
(
x; y
) exist? If so, what is it? If not, why not?
(2) Let
~v
=
h
1
;
3
i
and
f
(
x; y
)=
x
2
y
+
y
2
.Calculate the directional derivative of
f
(
x; y
)
in the direction
~v
at the point (1
;
,
1).
