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e106k - Exam I and Key MAC 2312 Feb 6 2006 S Hudson Show...

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Exam I and Key Feb 6, 2006 MAC 2312 S Hudson Show all your work. Use the space provided, or leave a note. Don’t use a calculator or your own extra paper. Problems 3-8 are worth 10 points each. 1) [5 points each] Short calculations. Simplify any easy terms like sin( π ) and e 0 . 20 k =2 1 k - 1 k - 1 = 20 k =0 2 k = (Hint: S - rS = a - ar n +1 ). d dx [ x 1 ln( t ) dt ] d dx [ x 2 1 ln( t ) dt ] 2) [5pts each] Compute the integrals: π/ 6 0 tan(2 θ ) . π/ 4 0 sec 2 ( θ ) . 2 t dt π 0 sin 2 3 x dx 3) Find the volume of the solid that is obtained when the region under the curve y = x over the interval [1,4] is revolved around the x -axis. 4) Find all values of x * in [-3,1] that satisfy the Mean-Value Theorem for f ( x ) = | x | . 5) Use left-hand endpoints, with n=3, to approximate the area under f ( x ) = 1 /x on [1 , 4]. 6) Find the area between the parabolas, y = 2 x - x 2 and y = 2 x 2 - 4 x . 7) Find the displacement and the distance travelled, given a ( t ) = t - 2, v 0 = 0, 1 t 5. 8) Choose ONE. Explain thoroughly. You can continue on the back.
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