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Unformatted text preview: Math 115 Final Exam April 20, 2007 Name: SOLUTIONS Instructor: Section Number: 1. Do not open this exam until you are told to begin. 2. This exam has 10 pages including this cover. There are 9 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 exam 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 two 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 show how you arrived at your solution. 8. Please turn off all cell phones and pagers and remove all headphones. Problem Points Score 1 10 2 12 3 12 4 12 5 16 6 12 7 12 8 8 9 6 Total 100 2 1. (2 points each, no partial credit) For the following statements circle True or False. Circle True only if the statement is always true. (a) If y is differentiable for all x , then the value of y ( x ) is a unique number for each x . True False (b) The only antiderivative of cos( x ) is sin( x ). True False (c) For a continuous function f on the interval a x b , if the lefthand sum and the righthand sum are equal for a given number of subdivisions, then they are equal to integraldisplay b a f ( x ) dx. True False (d) For the continuous function f , if the units of t are seconds and the units of f ( t ) are meters, then the units of integraldisplay 1 f ( t ) dt are meter seconds. True False (e) For any function f , if lim x 3 f ( x ) = a and lim x 3 + f ( x ) = a, then f (3) = a. True False 3 2. (12 points) Suppose that f and g are continuous functions and integraldisplay 2 f ( x ) dx = 5 and integraldisplay 2 g ( x ) dx = 13. Compute the following. If the computation cannot be made because something is missing, explain clearly what is missing....
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This note was uploaded on 04/01/2008 for the course MATH 115 taught by Professor Blakelock during the Winter '08 term at University of Michigan.
 Winter '08
 BLAKELOCK
 Math

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