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Fall 2005 Solutions - MATH 115 FIRST MIDTERM EXAM NAME...

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MATH 115 — FIRST MIDTERM EXAM October 11, 2005 NAME: SOLUTION KEY INSTRUCTOR: SECTION NO: 1. Do not open this exam until you are told to begin. 2. This exam has 9 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 other sound devices, and remove all headphones. PROBLEM POINTS SCORE 1 12 2 12 3 4 4 12 5 12 6 10 7 12 8 12 9 5 10 9 TOTAL 100
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2 1. (2 points each, no partial credit) Circle “True” or “False” for each of the following problems. Circle “True” only if the statement is always true. No explanation is necessary. (a) If A and B are positive constants, then the function f ( x ) = log( | Ax + B | ) has a vertical asymptote at x = B/A . True False (b) If an exponential function of t , in years, has decreased to 60% of the original value in two years, in four years it will decrease to 30% of the original value. True False (c) If h ( x ) = 1 . 3(0 . 5) x then the derivative, h , is decreasing for all x . True False (d) The functions sin( e x ) and e sin ( x ) are inverses of each other. True False (e) If w is a continuous function for all x , then lim h 0 w ( x + h ) w ( x ) h exists for all x . True False (f) If f ′′ ( x ) > 0 on the interval [ a, b ], then the average rate of change of f ( x ) on the interval [ a, b ] is greater than f ( x ) for all a < x < b . True False
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3 2. (12 points) The graph of the derivative function, f , is given below. List all of the marked x -values, if any, from the figure for which the following statements are true. If no marked x -values apply, write “none.” f ( x ) x y x 1 x 2 x 3 x 4 x 5 (a) The value of f ( x ) is greatest
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