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N the taylor polynomial example find the 1st 3rd and

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Unformatted text preview: ) around x=a: f ' ' ( a) 2 T2 ( x ) = f ( a) + f ' ( a)( x − a) + ( x − a) 2 because the € degree is 2 € QuadraBc ApproximaBons Example: •  1 . Let f ( x ) = 1+ x € 7.5 5 € -10 Find the quadraBc approximaBon to f(x) around x=1. 1 f ( x) = x +1 -7.5 -5 2.5 -2.5 0 2.5 5 7.5 The Taylor Polynomial Suppose the ﬁrst n derivaBves of the funcBon f are deﬁned at x=a. Then the Taylor polynomial of degree n matching the values of the ﬁrst n derivaBves is f ' ( a) f ' ' ( a) Tn ( x ) = f ( a) + ( x − a) + ( x − a) 2 + 1! 2! nth derivaBve f ( i ) ( a) f ( n ) ( a) + ( x − a) i + + ( x − a) n i! n! The Taylor Polynomial Example: Find the 1st...
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This note was uploaded on 03/03/2014 for the course MATH 1LS3 taught by Professor Lovric during the Winter '09 term at McMaster University.

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