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Unformatted text preview: MATH 115 FIRST MIDTERM EXAM October 13, 2004 NAME: SOLUTION KEY INSTRUCTOR: SECTION NO: 1. Do not open this exam until you are told to begin. 2. This exam has 10 pages including this cover. There are 10 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 2 sides of a 3 by 5 note card. 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 remove all headphones. PROBLEM POINTS SCORE 1 12 2 9 3 6 4 4 5 9 6 11 7 10 8 14 9 12 10 13 TOTAL 100 2 Midterm 1 Solutions 1. (2 points each) Circle True or False for each of the following problems. Circle True only if the statement is always true. No explanation is necessary. (a) log 1 ( x ) = 1 e x . True False (b) If a function is continuous at a point a , then it must also be differentiable at a . True False (c) Suppose f is a continuous function on the interval [5 , 8] and that f (5) = 2 and f (8) = 3. Then f has a zero on the interval (5 , 8). True False (d) lim x 6  x 7  x 7 exists and is equal to 1. True False (e) Suppose f is a continuous function and f is concave up on the interval ( 10 , 10). If f (1) = 2, it is possible that f (4) = 3. True False (f) Suppose f is a continuous function, f (1) = 6, and f ( x ) > 0 for all x between 0 and 5. Then it is possible that f (4) = 6. True False 3 2. (9 points) On the axes below, sketch a graph of a single function , g , with all of the following properties. g ( 2) = g (2) = 1 g ( x ) = 0 for x < 2 and x > 2 g ( x ) < 0 for 2 < x < 2 lim x  2 + g ( x ) = and lim x 2 g ( x ) = g 00 ( x ) > 0 for 2 < x < g 00 ( x ) < 0 for 0 < x < 2 x y g ( x ) 4 3. (6 points) A group of researchers in Costa Rica is studying the number of resplendent quetzals (these are birds) that nest in Monteverde Cloud Forest Preserve each year. The function f gives the number of quetzals the researchers count in the park on day t . Write an expression involving f that models each of the situations (a)(c) below....
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This note was uploaded on 09/11/2008 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.
 Fall '08
 BLAKELOCK
 Math, Calculus

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