WW3 - the function f ( x ) = 3cos ( . 6 x ) at a = 0. A....

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Jignesh Patel Assignment 3 MATH262, Fall 2010 due 10/13/2010 at 11:59pm EDT. 1. (1 pt) The function f ( x ) = 1 ( 1 - 7 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 = . 2. (1 pt) The function f ( x ) = 7 x arctan ( 3 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 = . 3. (1 pt) Compute the 9th derivative of f ( x ) = cos ( 4 x 4 ) - 1 x 7 at x = 0. f ( 9 ) ( 0 ) = Hint: Use the MacLaurin series for f ( x ) . 4. (1 pt) Find the degree 3 Taylor polynomial T 3 ( x ) of func- tion f ( x ) = ( 3 x + 4 ) 5 / 4 at a = 4. T 3 ( x ) = 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 6. (1 pt) Let T 5 ( x ) be the fifth degree Taylor polynomial of
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Unformatted text preview: the function f ( x ) = 3cos ( . 6 x ) at a = 0. A. Find T 5 ( x ) . (Enter a function.) T 5 ( x ) = B. Find the largest integer k such that for all x for which | x | < 1 the Taylor polynomial T 5 ( x ) approximates f ( x ) with error less than 10-k . k = 7. (1 pt) Let F ( x ) = Z x sin ( 3 t 2 ) dt . Find the MacLaurin polynomial of degree 7 for F ( x ) . Enter a function of x . Use this polynomial to estimate the value of Z . 63 sin ( 3 x 2 ) dx . Enter a number. 8. (1 pt) Evaluate lim x ln ( 1-4 x )+ 4 x + 8 x 2 3 x 3 Hint: Use power series. 1 Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 2...
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WW3 - the function f ( x ) = 3cos ( . 6 x ) at a = 0. A....

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