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SeriesPowerTaylorRcg

# SeriesPowerTaylorRcg - Mike Truong WeBWorK problems 1(1 pt...

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Mike Truong WeBWorK @ Dept of Mathematics and Statistics @ SDSU WeBWorK problems. WeBWorK assignment 15SeriesPowerTaylorRcg due 05/07/2008 at 10:00am PDT. 1. (1 pt) Compute the 6th derivative of f ( x ) = arctan x 2 5 at x = 0. f ( 6 ) ( 0 ) = Hint: Use the MacLaurin series for f ( x ) . Correct Answers: -1.92 2. (1 pt) Find the degree 3 Taylor polynomial T 3 ( x ) of func- tion f ( x ) = ( 3 x - 4 ) 4 / 3 at a = 4. T 3 ( x ) = Correct Answers: 16 + 8 * (x-4) + 1/2 * (x-4)**2 + -0.25/6 * (x-4)**3 3. (1 pt) Let T 5 ( x ) be the fifth degree Taylor polynomial of the function f ( x ) = cos ( 0 . 8 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 1 10 k . k = Correct Answers: (1 - .5*( (0.8*x)ˆ2) + ((0.8*x)ˆ4)/24 ) 3 4. (1 pt) Let F ( x ) = Z x 0 sin ( 5 t 2 ) dt . Find the MacLaurin polynomial of degree 7 for F ( x ) . Use this polynomial to estimate the value of Z 0 . 77 0 sin ( 5 x 2 ) dx . Correct Answers: 5 * xˆ3 / 3 - 5ˆ3 * xˆ7 / 42 0.283253712296042 5. (1 pt) Let F ( x ) = Z x 0 e - 5 t 4 dt .

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SeriesPowerTaylorRcg - Mike Truong WeBWorK problems 1(1 pt...

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