151review1F09

151review1F09 - Math 151 Fall 2009 Review Problems for Exam...

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Math 151, Fall 2009, Review Problems for Exam 1 Your first exam is likely to have problems that do not resemble these review problems. (1) Describe the set S = { x R : | 2 x - 4 | > 2 and | x - 3 | ≤ 1 } in terms of intervals. (2) Assume that f ( x ) is a function with domain R , and that f ( x ) is increasing on [5 , ). Explain why (a) and (b) must be true: (a) If f ( x ) is an odd function then f ( x ) is increasing on ( -∞ , - 5]. (b) If f ( x ) is an even function then f ( x ) is decreasing on ( -∞ , - 5]. (3) Complete the square for 2 x 2 - 8 x - 10. Use your answer to find the minimum of 2 x 2 - 8 x - 10 and to solve 2 x 2 - 8 x - 10 = 0. (4) Find functions f ( x ) and g ( x ) with domain R such that f g 6 = g f . (5) Find all solutions of 2 sin 2 x = 1 + cos(2 x ) in the interval [0 , 2 π ]. (6) Simplify sec(sin - 1 x ) and cos(tan - 1 x ). (7) Solve ln( x 2 + 7) - ln( x 2 + 1) = 2 ln 2. (8) The position of a particle at time t (in seconds) is given by t 1 + t 2 (in feet). Find the average velocity of the particle over the time interval [1 , 3].

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