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Unformatted text preview: April 2005 Mathematics 103 Name Page 2 of 10 pages Marks 1. Multiple Choice Questions: Select ONE correct answer (a, b, c, d, or e) for each question and write it in the table at the bottom of the page. You will not be graded for any work or answers outside those boxes. (Q1) The value of the integral Z 1 e ( x +e x ) dx is (a) e ( x +e x +1) ( x + e x + 1) (b) e e e (c) e e + e (d) e e+1 (e) (1 e)e (Q2) An antiderivative of x 4 x 2 dx is (a) 1 4 arctan( x/ 2) (b) 1 2 x arctan( x/ 2) (c) 1 2 ln  2 + x   2 x  (d) 1 2 ln  4 x 2  (e) 1 2 ln  4 x 2  (Q3) An approximation to the integral Z 2 arctan( x ) dx using n rectangles would be (a) 2 X k =0 arctan( k ) (b) n X k =1 arctan( k n ) (c) 2 n n X k =1 arctan( k n ) (d) 1 n 2 X k =0 arctan( k n ) (e) 2 n n X k =1 arctan( 2 k n ) (Q4) The value of the integral Z e 1 ln( x ) x 2 dx is (a) 1 2 e (b) 1 + 2 e (c) 1 (d) 1 e 2 1 (e) ln(e) e 2 ln(1) (Q5) Consider a mass density function d ( x ) = 4 x 2 over the interval 0 x 2. The centre of mass of this mass distribution is at (a) 1 (b) 4 (c) 4 3 (d) 3 4 (e) 16 3 Q1 Q2 Q3 Q4 Q5 NOTE: carefully check to ensure that you have correctly matched the response with the relevant questions. Only answers in this table using letters a, b, c, d, or e will be graded for Problem 1. Illegible or ambiguous responses will not receive marks. Continued on page 3 April 2005 Mathematics 103 Name Page 3 of 10 pages [10] 2. A certain random variable X takes values in the interval 0 x 2, with probability density p ( x ) = 1 x/ 2. Find the mean and variance of X . Mean = Variance = Continued on page 4 April 2005 Mathematics 103 Name Page 4 of 10 pages [12] 3. Consider the cumulative distribution function, F ( x ) on 0 x 10 shown in Figure 1....
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 Winter '10
 Dr.AlejandroCortas
 Math

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