1
MATH 203 Final Exam
December 18, 2008
Instructions:
Complete every question in Part I (Questions 17.)
Complete three of
the five questions in Part II (Questions 812). Each question is worth 10 points.
No calculators or other electronic devices may be used during the examination. Answers
may be left in terms of
√
7
,
sin(3)
, π
etc. Proctors will confiscate any devices observed
in the examination room. Give reasons for all answers. This exam will last 2 hours and
15 minutes. Good luck!
PART I: Answer all parts of Questions 17. Each question is worth 10 points
1.
(a) Parameterize the line that passes through the point (4
,
0
,

3) which is parallel
to the intersection of the plane 2
x

y
+
z
= 2 and the plane
x

3
z
= 4
(b) Find an equation of the plane perpendicular to the planes 2
x

y
+
z
= 2 and
x

3
z
= 4 that passes through (4
,

2
,
3)
.
2. Let
f
(
x, y, z
) =
x
2
y
+
y
2
z.
(a) Evaluate
∇
f
.
(b) Find an equation of the tangent plane to the surface
x
2
y
+
y
2
z
=

1
at the point (2
,

1
,
3).
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 Spring '11
 Ocken
 Math, Power Series, Taylor Series, Mathematical Series, Mathematical analysis, surface x2

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