Math_103_April_2005

Math_103_April_2005 - April 2005 Mathematics 103 Name Page...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Page1 / 10

Math_103_April_2005 - April 2005 Mathematics 103 Name Page...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online