MATH 241 Final Examination
Drs. M. Grillakis, D. Margetis, and J. Rosenberg
Monday, December 14, 2009
Instructions.
Answer each question
on a
separate
answer sheet
. Show all your work. A correct answer
without work to justify it may not receive full credit.
Be sure your name, section number, and problem
number are on each answer sheet, and that you have copied and signed the honor pledge on the first answer
sheet.
The point value of each problem is indicated. The exam is worth a total of 200 points. In problems
with multiple parts, whether the parts are related or not, the parts are graded independently of one another.
Be sure to go on to subsequent parts even if there is some part you cannot do. Please leave answers such as
5
√
2
or
3
π
in terms of radicals and
π
and
do not convert to decimals
.
You are allowed use of one sheet of notes. Calculators are not permitted.
1.
(a) (10 points) Find the area of the triangle with vertices
(1
,

1
,
1)
,
(1
,
2
,
3)
,
(2
,

1
,
2)
.
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 Spring '08
 staff
 Math

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