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# epe1 - Exam I MAC 2312 S Hudson Name Show all your work Use...

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Exam I Jan 30, 2003 MAC 2312 S Hudson Name Show all your work. Use the space provided, or leave a note. Don’t use a calculator or your own extra paper. 1) Short calculations, 5 pts each. Simplify any easy terms like sin( π ) and e 0 . a) d dx [ x 0 sec 2 ( t ) dt ] b) 4 0 x + e x dx c) 2 1 1 t dt d) π/ 2 0 sin 2 x cos x dx 1

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e) 3 0 | x - 2 | dx = f) Find the average value of f ( x ) = x 3 on the interval [0,5]. g) 4 0 dx 2 x +1 = h) π 0 sin 2 3 x dx i) Find the area between the parabolas, y = 2 x - x 2 and y = 2 x 2 - 4 x . j) Use left-hand endpoints to find A 2 for f ( x ) = sin( x ) on [0 , π/ 2]. 2
2) (10pts) Rosanne drops a ball from a height of 400 ft. The force of gravity is 32ft/s/s, which is the acceleration on the ball. So, the velocity is - 32 t (or, you might use 32 t ). a) Find a formula for the height of the ball h ( t ) after t seconds. Be sure to show all your work and reasoning, and check that h (0) = 400. b) How many seconds until the ball hits the ground? (This occurs when h=0, of course). 3) (10pts) a) Let f ( x ) = x 2 on [0,2]. Use the well-known formula n ( n + 1)(2 n + 1) / 6 to calculate and simplify the Riemann Sum below. Answer in terms of n n i =1 f ( x i x b) Find the exact area under this curve by taking a limit as

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