FinalExam_W10_Solutions

FinalExam_W10_Solutions - Math 115 Final Exam April 23,...

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Math 115 — Final Exam April 23, 2010 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 10 pages including this cover. There are 9 problems. Note that the problems are not of equal diFculty, so you may want to skip over and return to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI-92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. You are also allowed two sides of a 3 ′′ × 5 ′′ note card. 7. If you use graphs or tables to ±nd an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn of all cell phones and pagers , and remove all headphones. 9. Use the techniques oF calculus to solve the problems on this exam. Problem Points Score 1 12 2 12 3 12 4 12 5 8 6 14 7 10 8 12 9 8 Total 100
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Math 115 / Final (April 23, 2010) page 2 1 . [12 points] For the following statements, select True if the statement is ALWAYS true, and select False otherwise. No explanations are required. a . [2 points] If f is a di±erentiable function and f (5 . 1) f (5) 0 . 1 = - 3, then f (5) = - 3. True False b . [2 points] If g is a continuous function, then i 20 1 g ( x ) dx = i 100 1 g ( x ) dx + i 20 100 g ( x ) dx . True False c . [2 points] If h is an odd function and is continuous everywhere, then h is invertible. True False d . [2 points] If k is a di±erentiable function and is always concave up, then k ( a ) k ( b ) - k ( a ) b - a whenever a < b . True False e . [2 points] If is a continuous function, then i 3 2 ( t ) dt i 4 2 ( t ) dt . True False f . [2 points] Suppose m is a twice di±erentiable function. If m ′′ (5) = 0, then m does not have an in²ection point at x = 5. True False
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Math 115 / Final (April 23, 2010) page 3 2 . [12 points] Use the graph of the function f and the table of values for the function g to answer the questions below. Each problem requires only a small amount of work, but you must show it. 1 2 3 4 5 6 10 20 30 f ( x ) x -20 -10 0 10 20 30 g(x) 0 4 0 -18 -56 -120 g’(x) 6 1 -10 -27 -50 -79 a . [3 points] Write a formula for the local linearization of g near x = 10 and use it to ap- proximate g (10 . 1).
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FinalExam_W10_Solutions - Math 115 Final Exam April 23,...

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