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Unformatted text preview: x ) = cos x for x near 0. Ans. f ( x ) = cos x ⇒ f ( ) = 1 f ( x ) =sin x ⇒ f ( ) = f 00 ( x ) =cos x ⇒ f 00 ( ) =1 f 000 ( x ) = sin x ⇒ f 000 ( ) = f ( 4 ) ( x ) = cos x ⇒ f ( 4 ) ( ) = 1 f ( 5 ) ( x ) =sin x ⇒ f ( 5 ) ( ) = f ( 6 ) ( x ) =cos x ⇒ f ( 6 ) ( ) =1 Thus, the Taylor polynomial of degree 6 approximating f ( x ) = cos x for x near 0 is P 6 ( x ) = 11 2 x 2 + 1 4! x 41 6! x 6 . 1 Note : Taylor polynomial of degree n approximating f ( x ) for x near 0 is f ( x ) ≈ P n ( x ) = f ( ) + f ( ) x + f 00 ( ) 2! x 2 + f 000 ( ) 3! x 3 + f ( 4 ) ( ) 4! x 4 + ··· + f ( n ) ( ) n ! x n...
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 Spring '07
 Hohnhold
 Math, Mean, dx, C. Ans

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