Problems_Guide

Problems_Guide - The Ultimate Guide David Imberti 1...

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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 super-hard 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 rope-bridge 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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Problems_Guide - The Ultimate Guide David Imberti 1...

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