David Imberti
April 16, 2010
1 Introduction
The following is a complete list and then worked out solutions over all the quizzes I have given you ever
during this course. Some of these quiz questions you may not have seen. This is because sometimes I
end up cutting or changing a quiz question for one of my sections after seeing how it fared for the other
section, sometimes one section has more time than another, or sometimes sometime (huh, weird
grammar) before class I decide to cut out a question or replace it with a diﬀerent one. As such, this list
may be bigger than you expected. Also, sometime in the middle of the semester my ﬁling system
apparently got shuﬄed, so this list may not be in order either. BUT, at the very least, it should be more
complete.
Not only quiz questions, but at the beginning of the semester I made ’bonus’ problems (which didn’t
seem to have a lot of interest, so I stopped making them after the second week or so) which I include the
worked out solutions here. ALSO are worked out solutions to the ’bonus’ problems from the practice
exams I made you guys. I had them worked out for the ﬁrst and second practice exam, but lost the
second practice exam’s solutions, so I remake them here.
Finally, since the quiz questions are intermingled with the bonus problems and practice exam problems,
and a lot of things are out of order: THE DIFFICULTY WILL VARY TREMENDOUSLY. Don’t be
worried if you can’t get one of these immediately! Just assume that it’s one of my superhard bonus
problems and move on. My suggestion would be to go through and do the ones you can do quickly ﬁrst
to boost your conﬁdence, then start at the beginning of the list again to see which ones you can quickly
do again, then start at the beginning of the list and slog through.
If you see any problems with these problems, be sure to let me know. Or if there are any good ones/quiz
problems that I forgot to put up, give me a statement and I’ll put them up with solution hopefully.
tl;dr:
The ﬁrst section is a list of problems. The second section is a list of solutions. Do the problems without
looking at the solutions. If you get stuck look at the solutions. Take your time. You’ve got two weeks
from the ﬁnal from the time when I ﬁrst put these problems up.
2 The List
(1)
F
(
θ
) =
< cos
(
θ
)
,sin
(
θ
)
>
(a) Calculate

F
(
θ
+
2
π
n
)

F
(
θ
)

(b) Find lim
n
→∞

F
(
θ
+
2
π
n
)

F
(
θ
)

(c) Suppose
f
is continuous. What is lim
n
→∞

< f
(
x
+
1
n
)
,f
(
x
+
1
n
)
>

?
(2) An anvil is placed on the exact center of a ropebridge weighing 2000 lbs. The edges of the bridge
bow in at 30 degrees. What is the tension on each end of the bridge? (assume the bridge’s weight is
neglible)
(3) Find the angle between the face of a cube and its diagonal.
(4) Let
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 Spring '09
 Power Series, dx, Σ∞

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