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Unformatted text preview: Exam I Sept 13, 2007 MAC 2312 S Hudson Problems 4-8 are worth 10 points each. 1) [20 points; 4 each] Short calculations. Notice that the second sum starts at 11. 20 k =1 k 2 = 30 k =11 k = 2007 k =1 ( 1 k- 1 k +1 ) = d dx [ R x 3 ln( t ) dt ] d dx [ R x 2 1 ln( t ) dt ] 2) [15pts] Compute these integrals: R / 4 sec 2 ( ) d . R 3 | ( x- 2)( x + 1) | dx R sin 2 3 x dx 3) [15pts] Answer True or False: In uniformly accelerated motion, velocity is constant. For continuous functions, R b a f ( x ) g ( x ) dx = ( R b a f ( x ) dx ) ( R b a g ( x ) dx ). If we used only regular partitions of [a,b], then the phrase max 4 x k 0 would be equivalent to n + . If f is bounded on [a,b] it is integrable there. If we use the Right Endpoint Rule to approximate R 2 1 1 t dt , with n = 100, our estimate will be too small. 4) Find all values of x * that satisfy the Mean-Value Theorem for Integrals, for f ( x ) = | 2 x | on the interval [-1,3]. 5) Use left-hand endpoints in a regular partition, with n=3, to approximate the area under f ( x ) = x 2 + 1 on [1 , 4]....
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