M101Final200804 - April 2008 Mathematics 101 Page 2 of 11...

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Unformatted text preview: April 2008 Mathematics 101 Page 2 of 11 pages Marks [21] 1. Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answers. Unless otherwise stated, simplify your answer as much as possible. (a) Evaluate Z x 3- 2 x x dx . Answer (b) Evaluate Z (4 sin - 3 cos ) d . You must simplify your answer completely . Answer (c) Express lim n 1 n n X i =1 1 1 + ( i/n ) 2 as a definite integral. Do not evaluate this integral. Answer Continued on page 3 April 2008 Mathematics 101 Page 3 of 11 pages (d) Write down the Trapezoidal Rule approximation T 3 for Z 4 1 x cos( /x ) dx . Leave your answer expressed as a sum involving cosines. Answer (e) Let f ( x ) = kx 2 (1- x ) if 0 x 1 and f ( x ) = 0 if x < 0 or x > 1. For what value of the positive constant k is f ( x ) a probability density function? Answer (f) Find the first three nonzero terms in the power-series representation in powers of x (i.e. the Maclaurin series) for Z x t 1- t 8 dt . Answer (g) Let f ( x ) = Z x 3 x t sin t dt . Find f ( x ). Answer Continued on page 4 April 2008 Mathematics 101 Page 4 of 11 pages Full-Solution Problems. In questions 27, justify your answers and show all your work . If a box is provided, write your final answer there. Unless otherwise indicated, simplification of answers is not required....
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This note was uploaded on 10/26/2010 for the course MATH MATH100 taught by Professor Akos during the Spring '10 term at The University of British Columbia.

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M101Final200804 - April 2008 Mathematics 101 Page 2 of 11...

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