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MATH 203 Final Exam
December 19, 2007
PART I: Answer all parts of Questions 17. Each question is worth 10 points
Question 1
a) Find an equation of the plane that contains both the line
x

1
2
=
y

2
3
=
z

3
4
and the point (1
,
2
,
0).
b) Find parametric equations describing the line through the point (1
,
2
,
3) which is
perpendicular to the plane
z
=
x
+ 2
y

4.
Question 2
a) Given the curve
~
r
(
t
) =
<
√
t,
4
t
,
t
2
2
>
, ﬁnd a parameterization of the
tangent line at (2
,
1
,
8).
b) Find an equation of the tangent plane to the surface
x
3
z
2
+ 4(
y

1)
2
= 5 at the point
(1
,
2
,

1).
Question 3
Consider the function
f
(
x,y
) =
x
2
x
+ 3
y
.
a) Find the directional derivative of
f
(
x,y
) at the point P (2
,

1) in the direction toward
the point Q (

1
,
1).
b) Find the directional derivative in the direction of maximum increase of
f
(
x,y
) at the
point
P
.
Question 4
a) Let
R
be the region bounded by
y
=
x
,
y
= 2
x
and
y
= 6. Write
Z Z
R
f
(
x,y
)
dA
as
an iterated integral.
(b) Reverse the order of integration in the integral
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 Spring '11
 Ocken
 Math

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