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Name: Math 2260 Exam #2 March 9, 2012 Instructions: You are welcome to use one sheet of notes, but no other references or tools are allowed (no textbooks, no calculators, etc.). This is a 50 minute exam; you may start working at 10:10 am and must stop at 11:00 am. To receive full credit for a correct answer you must demonstrate how you arrived at that answer. To receive partial credit for an incorrect answer your work must be clearly explained. 1 1. Integrate Z x2 x dx. − 5x + 4 2 2. Does the improper integral Z ∞ xe−2x dx 0 converge or diverge? If it converges, find the value of the integral. 3 3. Evaluate the definite integral Z 1 √ 0 4 x2 dx. 1 − x2 4. Find an antiderivative for the function f (x) = e3x cos(x). 5 5. A super-fast-growing bacteria reproduces so quickly that the rate of production of new bacteria is proportional to the square of the number already present. If a sample starts with 100 bacteria, and after 3 hours there are 200 bacteria, how long after the starting time will it take until there are (theoretically) an infinite number of bacteria? 6