Assignment 8

Assignment 8 - x = a for each of the following be...

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Math 138 Assignment 8 Fall 2008 The following questions are to be answered neatly and completely on standard size (8.5 by 11 inch, or metric equivalent) paper. Please insure that your name and ID number are clearly indicated on each page, and that all your pages are securely fastened together, staples are preferred. This assignment is due at 9:00 a.m. on Friday, November 21, 2008 . 1. a) Determine the radius of convergence and the interval of convergence for the power series : X n =1 (2 - 3 x ) n n . Note: the series is not in standard power series form, but can be treated in the same manner. b) Determine the radius of convergence and the interval of convergence for the power series : X n =0 ( - 1) n n 4 2 2 n x n . 2. Let f ( x ) = x x 2 - 4 x + 3 . a) Determine a power series expansion for f ( x ) centred at 0, and find its radius of convergence. b) Determine a power series expansion for f ( x ) centred at 2, and find its radius of convergence. 3. Find the Taylor polynomial of order N , P N ( x ), centred at
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Unformatted text preview: x = a for each of the following be evaluating f ( a ) ,f ( a ) ,f ( a ) ,. .. to determine the coecients. a) f ( x ) = ln(1-x ) ,P 4 ( x ) ,a = 0 b) f ( x ) = cos x,P 3 ( x ) ,a = 3 4. Given the series X n =1 (2 x-1) n n b 2 n , where b > 0 is constant, nd the value(s) of b such that the series has radius of convergence R = 1, and determine the interval of convergence for such b . 5. Use a known series expansion to nd the Maclaurin series for f ( x ) = x 1 + x 2 , and then, by inspection, determine f (9) (0). Please note that assignments may be submitted to the drop box before the due date. Assignments will be removed from the drop box shortly after the time they are due. The drop boxes are located on the fourth oor of the Math and Computer building (MC) outside room MC 4066. Check the course outline for the box/slot for your assignment....
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