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Unformatted text preview: g ( x ) = π + 0 . 5 sin x 2 has a unique Fxed point on [0 , 2 π ]. (b) ±or p = π , compute p 1 . (c) How many iterations are necessary to achieve the accuracy 102 ? III. Let f ( x ) = x 26. (a) Prove that f has a positive zero p . (b) With p = 1, fnd p 2 by Newton’s iterations. IV. Let f ( x ) = cos x , x = 0, x 1 = 0 . 6 and x 2 = 0 . 9. (a) Construct an interpolation polynomial of degree at most two to approximate f . Use cos (0 . 6) = 0 . 8 and cos (0 . 9) = 0 . 6. (b) Use the Theorem of the course to Fnd an error bound for the approximation....
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This note was uploaded on 10/28/2010 for the course MATH 151a taught by Professor Staff during the Spring '08 term at UCLA.
 Spring '08
 staff
 Math

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