sample midterm2 2000 - Math 20 Prof Moore Winter 2000...

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Math 20 Winter 2000 Prof. Moore Sample Midterm 2 Directions: You may use a graphing calculator to graph and compute things during the exam, but you may not use any notes or books, or receive help from any other person. Show all of your work, explaining as much as possible. 1. The acceleration function for a particle moving along a line is given by a ( t ) = 3 t +2. If v (0) = - 5 is the initial velocity, find the velocity at time t . Also, find the distance traveled during the time interval [0 , 3]. What is the total displacement of the particle? 2. Express 5 2 (3 x - 1) dx as the limit of a sum. Evaluate this limit. You may use the facts that n i =1 i = n ( n + 1) 2 and n i =1 i 2 = n ( n + 1)(2 n + 1) 6 . 3. a) Find 6 1 x - 1 3 x 2 dx . b) What does the first part of the Fundamental Theorem of Calculus say? (You may use your own
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Unformatted text preview: c) Find d ds · s 2 Z s 3 ³ √ t-3 t 7 ´ dt ¸ . 4. Use Newton’s method to estimate √ 89 to six decimal places. Show each of your successive estimates. Write down a formula that gives you the estimate x 2 in terms of x 1 . 5. A ball is thrown directly upward at a speed of 64 feet per second from a cli± 80 feet above a beach. At what time does the ball reach its highest point? How high above the beach does it get? 6. a) Draw a direction field for the function f ( x ) = 9 x 2 . Use this direction field to sketch several members of the family of antiderivatives. b) Compute the general antiderivative for f ( x ) = 9 x 2 explicitly and sketch several specific an-tiderivatives....
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