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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 45 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 32 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 xx ) 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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 Spring '09
 HarvanshManocha
 Calculus, Taylor Series, #, Taylor Polynomial, Polytechnic Institute of NYU MA

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