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Unformatted text preview: Math 105 Final Exam December 17, 2009 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 14 pages including this cover. There are 10 problems. Note that the problems are not of equal difficulty, 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 TI92 (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. 7. If you use graphs or tables to find 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 off all cell phones and pagers , and remove all headphones. Problem Points Score 1 12 2 9 3 12 4 10 5 6 6 8 7 12 8 9 9 10 10 12 Total 100 Math 105 / Final (December 17, 2009) page 2 1 . [12 points] For each statement below, circle TRUE if the statement is always true. Otherwise, circle FALSE. You do not have to show any work for your answers. a . [2 points] The graph of every power function is concave up. True False b . [2 points] If g ( t ) is a periodic function, then the graph of g ( t ) has no vertical asymptotes. True False c . [2 points] The graph of f 1 ( x ) is obtained by reflecting the graph of f ( x ) across the xaxis. True False d . [2 points] The function f ( x ) = x is a power function. True False e . [2 points] When a graph of a polynomial function f ( x ) intersects the xaxis exactly 4 times, that means that f ( x ) has degree 4. True False f . [2 points] When a is negative, lim x x a = . True False Math 105 / Final (December 17, 2009) page 3 2 . [9 points] This past Thanksgiving, Emily decided to bake a pumpkin and sweet potato pie. In the recipe she used, the only two ingredients in the pie filling were pumpkin and sweet potato. The recipe required 12.5 ounces of pumpkin, but did not explicitly specify the amount of sweet potatoes to add. Let C = f ( x ) be the ratio of the volume of sweet potatoes to the total volume of filling when x ounces of sweet potatoes are used. Note that C = f ( x ) gives the concentration of sweet potatoes in the pie filling....
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This note was uploaded on 01/28/2012 for the course MATH 105 taught by Professor Rhea during the Fall '08 term at University of Michigan.
 Fall '08
 Rhea
 Math

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