03faex2v2 - Math 132 Exam 2 Name Section There are 100...

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Unformatted text preview: Math 132 December 11, 2003 Exam 2 Name: Section: There are 100 possible points on this exam. Be sure to read each question carefully and answer the question asked. Show your work neatly and clearly— answers without justiﬁcation will receive no credit. Partial credit may be given for a correct approach even if you don’t get to the right answer. Give exact answers unless otherwise asked. GOOD LUCK! 1. Simplify the following: a) 2‘1 b) 4% 2. Suppose I am given an unfair six—sided die, where P (1) = é, P (2) = i and P(3) : P(4) = P(5) = P(6) = 113. Hi tell this die twice, what is the probability that the product of the two rolls is four? 3. Determine the concavity of the following sets of points: (a) (1’4)? (-332)? (“577) (b) (0,0), (1, 2.2), (3,734) (0) (0,6), (1,7r + e), (7r,7r2 + 8) (Here, 6 is a constant, e > 0) 4. Consider the piecewise equations __ 2x+4 ifo—Z yl 3+2(a:—-3) ifas>~2 and _ 5 ifx§100 y2_ 227—195 ifm>100 (a) Is 3/; continuous? What about yg? (b) Find where yl : yg 5. The least integer function f (x) = is deﬁned {it} = smallest integer N so that a: g N. (a) Find {23.2}, {7r}, {-7r} and {—14}. (b) This function can be written as a piecewise function. Where are the “break points”? Explain. (note: you do NOT have to give a formula for this function) ...
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