MATH 141 Midterm: MATH141 PILACHOWSKI-T SPRING2007 0101 MID SOL 1
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15 Feb 2019
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March 2, 2007: a. (12 points) let. 7 and let [a, b] be the largest interval containing x = 0 such that f has an inverse function f on this interval. Find a and b. (you must show calculus work. ) f. 18 b. (4 extra points) you know that g(1) = 2, and ( 3: (14 points) use integration by substitution to evaluate . Let u = cos 2x, du = 2 sin 2x dx; x u. Note that the range of sin 1 u, [ cos dx. 1: a. (14 points) find the slope of the curve y x. Give an exact value answer in simplest form. 2ln y b. (14 points) find y lim x. Possible answers are a calculated numeric value, or dne (does not exist). You must show all your steps in order to receive full credit. Note: this procedure is dependent upon knowing that ln e x x x.
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