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WEBWORK 3

# WEBWORK 3 - Syed Shah due at 11:59pm EDT Assignment 3...

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Syed Shah Assignment 3 MATH262, Fall 2009 due 10/18/2009 at 11:59pm EDT. You may attempt each problem a maximum of 7 times. 1. (1 pt) The function f ( x ) = 1 ( 1 - 10 x ) 2 is represented as a power series f ( x ) = n = 0 c n x n . Find the first few coefficients in the power series. c 0 = c 1 = c 2 = c 3 = c 4 = Find the radius of convergence R of the series. R = . Correct Answers: 1 20 300 4000 50000 0.1 2. (1 pt) The function f ( x ) = 6 x arctan ( 5 x ) is represented as a power series f ( x ) = n = 0 c n x n . Find the first few coefficients in the power series. c 0 = c 1 = c 2 = c 3 = c 4 = Find the radius of convergence R of the series. R = . Correct Answers: 0 0 30 0 -250 0.2 3. (1 pt) Compute the 7th derivative of f ( x ) = cos ( 4 x 3 ) - 1 x 5 at x = 0. f ( 7 ) ( 0 ) = Hint: Use the MacLaurin series for f ( x ) . Correct Answers: 53760 4. (1 pt) Find the degree 3 Taylor polynomial T 3 ( x ) of func- tion f ( x ) = ( - 3 x + 15 ) 3 / 2 at a = 2. T 3 ( x ) = Correct Answers: 27 + -13.5 * (x-2) + 2.25/2 * (x-2)**2 + 0.375/6 * (x-2)**3 5. (1 pt) The Taylor series for f ( x ) = ln ( sec ( x )) at a = 0 is n = 0 c n x n . Find the first few coefficients. c 0 = c 1 = c 2 = c 3 = c 4 = Find the exact error in approximating ln ( sec ( 0 . 3 )) by its fourth degree Taylor polynomial at a = 0 . The error is Correct Answers: 0 0 0.5 0 0.0833333333333333 1.66559260579585E-05

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WEBWORK 3 - Syed Shah due at 11:59pm EDT Assignment 3...

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