1
MATH 203 Final Exam
May 18, 2009
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 line
L
is given parametrically by the equations
x
= 4
t
;
y
= 4;
z
= 2 +
t
.
(a) Compute all unit vectors parallel to the line.
(b) Compute the coordinates of the point where the line intersects the plane
P
with equation
x
+ 2
y
+ 3
z
= 0.
(c) Is the line
L
perpendicular to the plane
P
? Justify your answer.
2. Let
f
(
x,y,z
) =
x
2

cos(
xy
) +
e
yz
.
(a) At the point (3
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 Spring '11
 Ocken
 Math, Maclaurin Series, Taylor Series, plane tangent

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