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Unformatted text preview: 1 MATH 116 FINAL EXAM Fall 2004 NAME: ID NUMBER: INSTRUCTOR: SECTION NO: 1. Do not open this exam until you are told to begin. 2. This exam has 12 pages including this cover. There are 11 questions. 3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you turn in the exam. 4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about the problems during the exam. 5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 6. You may use your calculator. You are also allowed 2 sides of a 3 by 5 notecard. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to make clear how you arrived at your solution. 8. Please turn off all cell phones and devices whose sounds might disturb your classmates. Please remove all headphones. PROBLEM POINTS SCORE 1 16 2 6 3 5 4 6 5 10 6 15 7 5 8 6 9 10 10 8 11 13 TOTAL 100 2 1. (16 points) (a) If Z 1 f ( x ) dx = 2, then Z 2 f x 2 dx = . (b) Does the infinite series X n =1 2 n n ! converge or diverge? Justify your answer. (c) Is the function te 2 t a solution of the differential equation dy dt + 2 y e 2 t = 0 ? Explain why or why not. (d) Suppose C ( t ) is the daily cost of heating your house, measured in dollars per day, where t = 0 corresponds to January 1, 2004. Give the meaning, in words, of each of the following quantities. (i) Z 60 C ( t ) dt . (ii) 1 60 Z 60 C ( t ) dt . 3 2. (6 points) Write a parametrization for each of the following curves in the xyplane....
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This note was uploaded on 01/28/2012 for the course MATH 146 taught by Professor Conger during the Winter '08 term at University of Michigan.
 Winter '08
 Conger
 Math, The Land

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