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final174gradW09 - -2 0 | f x-p x | ≤ h 2 2 where h = x i...

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Math 274 Final March 16, 2009 Please put your name, ID number, and sign and date. There are 2 problems worth a total of 50 points. You must show your work to receive credit . Print Name: Student ID: Signature and Date: Problem Score 1 /25 2 /25 Total /50 1

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1. (25 pts) Consider data points taken from f ( x ) = e 2 x at n evenly spaced points: - 1 = x 1 < x 2 < . . . < x n = 0 . Let p ( x ) be the piecewise linear polynomial interpolating these points. (a) Use calculus

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Unformatted text preview: -2 , 0]: | f ( x )-p ( x ) | ≤ h 2 2 , where h = x i +1-x i . 2 (b) Use this bound to ﬁnd a condition on n that will ensure | f ( x )-p ( x ) | ≤ 10-4 . 3 2. (25 pts) Let F ( x ) = Z x x f ( x ) dx. Use Taylor series to ﬁnd the leading term of the absolute error of Midpoint rule in one subinterval: ± ± ± ± ± Z x + h x f ( x ) dx-hf ( x + h/ 2) ± ± ± ± ± . 4...
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