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Winter 2005 Solutions

# Winter 2005 Solutions - MATH 115 FIRST MIDTERM EXAM...

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MATH 115 — FIRST MIDTERM EXAM February 8, 2005 NAME: SOLUTION KEY INSTRUCTOR: SECTION NO: 1. Do not open this exam until you are told to begin. 2. This exam has 8 pages including this cover. There are 8 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 16 4 15 5 8 6 5 7 14 8 18 TOTAL 100

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2 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) Every continuous function is differentiable. True FALSE (b) If f ( x ) > 0 for all x in the interval ( a, b ), then f is increasing on the interval ( a, b ). TRUE False (c) By definition, the instantaneous velocity is equal to a difference quotient. True FALSE (d) Every rational function has a vertical asymptote. True FALSE (e) If a function is not continuous at a point, then it is not defined at that point. True FALSE (f) If a function f is decreasing on an interval, then f is decreasing on that interval. True FALSE
3 2. (7+2+3 points) (a) On the axes below, sketch a graph of a single, continuous, differentiable function , g , with all of the following properties.

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