14-1350-AKT Makeup Final
April-30-14
2:14 PM
You have 3 hours to write this exam. Answer the following 3 questions. 
Readability matters! The ideal solution of each of the above problems should look like the best explanation of the answer one could give on about 3 pages of a typical math book (with some space taken by formulas and drawings), except the handwritten version may be shorter or longer, depending on your handwriting.