FINAL EXAM
Math 51, Spring 2001.
You have 3 hours.
No notes, no books.
YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING
TO RECEIVE CREDIT
Good luck!
Name
ID number
1.
(/50 points)
2.
(/50 points)
3.
(/50 points)
4.
(/50 points)
5.
(/50 points)
Bonus
(/20 points)
Total
(/250 points)
“On my honor, I have neither given nor
received any aid on this examination. I
have furthermore abided by all other
aspects of the honor code with respect to
this examination.”
Signature:
Circle your TA’s name:
Kuan Ju Liu (2 and 6)
Robert Sussland (3 and 7)
Hunter Tart (4 and 8)
Alex Meadows (10)
Dana Rowland (11)
Circle your section meeting time:
11:00am
1:15pm
7pm
1
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View Full Document1. Let the function
f
:
±
R
2
 {
→
0
}
²
→
R
2
have components
f
1
and
f
2
as described by
f
³
x
y
´
=
³
f
1
f
2
´
=
³
(
x
2
)
y
xy
2
´
(a) Note that the function
f
is not deﬁned at the origin; this is because the component
f
1
is not deﬁned there.
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 '07
 Staff
 Math, Linear Algebra, Algebra, Derivative, Differential Calculus, Trigraph, Continuous function, Vector Motors, row space, Kuan Ju Liu

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