Pre-Calc Homework Solutions 373

# A since f is a cubic polynomial it is its own taylor

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Unformatted text preview: mial of order 3. P3(x) 2x 3 x 2 3x 8 or 8 3x x 2 2x 3 (b) f (1) 2x 3 6x 2 12x 12 x 1 2 2 2 2 2 2 2 x 12 x x x 4 2 2 4 2 4 4 3 2 x2 2x 2 3x 3 8 x 1 x 1 2 4 2 4 x x f (1) f (1) f (1) P3(x) 11 f (1) 2! 4 2 x 1 14, so 7 4 f (1) 12, so 3! 2 1)2 2(x 1)3 2 11(x 1) 7(x 11. f f f 4 4 4 cos x x /4 15. (a) Since f (0) f (0) f (0) f (0) polynomial of order 3 is P3(0) 0. 2 2 2 2 f 0, the Taylor sin x cos x x /4 x /4 , so f 4 4 2 4 2 12 (b) f (1) f (1) f (1) f (1) x4 x 1 1 4 12, so 24, so 1) 8 2 x 2! f (1) 2! f (1) 3! 2! 4x 3 x 1 f 4 sin x 2 2 2 2 2 2 2 2 2 x /4 2 , so 3! 12x 2 24x 1 4 4 x 1 6 4 1)2 4(x 1)3 P0(x) P1(x) P2(x) P3(x) x 1 2 2 2 2 2 2 2 x 12 x x x 4 4 2 4 4 3 2 P3(x) 4 2 4 4(x 5x 5x 6(x x x 4 2 16. (a) P3(x) 6 3 x 3! 4x 2 4.848 x3 4 f (0.2) P3(0.2)...
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## This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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