1124worksheet11

1124worksheet11 - x = 0 by the sixth degree Taylor...

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Polytechnic Institute of NYU MA 1124/1424 Worksheet 11 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 15 3 10 4 10 5 15 6 10 7 10 8 10 9 10 Total 100 1
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2 (1) Find the radius of convergence and the interval of convergence of the series. (a) X n =0 x n n + 2 (b) X n =1 n 5 n x n
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3 (2) Find the radius of convergence and the interval of convergence of the series. (a) X n =1 ( x - 4) n n 5 n (b) X n =1 ( - 1) n ( x - 1) n n
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4 (3) Find the radius of convergence and the interval of convergence of the series. (a) X n =0 2 n ( x - 3) n n + 3 (b) X n =1 (2 x - 1) n n 3
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5 (4) Find the radius of convergence and the interval of convergence of the series. (a) X n =1 n n - 1 ( x + 2) n 2 n (b) X n =1 ( - 1) n 2 3 n ( x + 1) n
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6 (5) Construct the Taylor polynomial of degree 5 for the function about the point a . (a) f ( x ) = cos x , a = π/ 4 (b) f ( x ) = 1 /x , a = 2
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7 (6) The function f ( x ) is approximated near
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Unformatted text preview: x = 0 by the sixth degree Taylor polynomial P 6 ( x ) = 2 x + 4 x 3 + 2 x 4-5 x 5 + 6 x 6 Give the value of (a) f (0) (b) f (0) (c) f 00 (0) (d) f (3) (0) (e) f (4) (0) (f) f (5) (0) (g) f (6) (0) 8 (7) Find the Taylor polynomial of the function f for the given values of a and n . (a) f ( x ) = 3 x 3-2 x 2 + 4 x + 1, a = 1, n = 3 (b) f ( x ) = cos πx , a = 1 / 3, n = 4 9 (8) Find the Taylor polynomial of the function f for the given values of a and n . (a) f ( x ) = ln x , a = 1, n = 5 (b) f ( x ) = arctan x , a = 1, n = 3 10 (9) Find lim x → (sin x-x ) 3 x 9 and simplify your answer. Hint: Use the first two nonzero terms of the Taylor polynomial for sin x ....
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