Exam2F10_Solns - Math 105 Second Midterm November 15, 2010...

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Unformatted text preview: Math 105 Second Midterm November 15, 2010 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 12 pages including this cover. There are 9 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 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. 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 6 2 14 3 12 4 10 5 14 6 10 7 10 8 12 9 12 Total 100 Math 105 / Exam 2 (November 15, 2010) page 2 1 . [6 points] x y The graph of f ( x ) The graph of f ( x ) is shown in the figure above. In each of the figures below, the graph shown represents a transformation of f ( x ). Note that the scale of the axes is the same in each of the graphs below as it is in the graph of f ( x ) above. For each figure, circle the one formula which best represents the given transformation. Jus- tification is not expected for these problems. x y x y x y i. f ( x + 2)- 2 ii. f ( x- 1)- 1 iii. 2 f ( x- 1) i. 0 . 5 f ( x )- 4 ii. f (- 2 x )- 2 iii.- . 5 f ( x ) i. f (- . 5 x ) + 2 ii. f (- 2 x ) + 1 iii.- f (- x ) + 4 Math 105 / Exam 2 (November 15, 2010) page 3 2 . [14 points] Note that calculator approximations will not receive credit when an exact answer is required. a . [5 points] Solve for t exactly in the equation 3 e t = 5 t . (Show your work step-by-step.) Solution: We can take the natural log of both sides of the equation and then use properties of logarithms to simplify the expressions: ln(3 e t ) = ln(5 t ) ln(3) + ln( e t ) = t ln(5) ln(3) + t = t ln(5) ln(3) = t ln(5)- t ln(3) = t (ln(5)- 1) ln(3) ln(5)- 1 = t Answer: t = ln(3) / (ln(5)- 1) b . [4 points] Suppose f is an even function and f (2) =- 3. Find the coordinates of two points that must lie on the graph of 2 f ( x- 1)....
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Exam2F10_Solns - Math 105 Second Midterm November 15, 2010...

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