Math 126 - TaylorHW1

# Math 126 - TaylorHW1 - . 7 10-4 . 8. (b) (0 . 1) n +2 ( n +...

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Homework 1 Selected Answers Math 126 1. T 0 2 ( x ) = 1 + x , T 00 2 ( x ) = 1. 2. T 0 3 ( x ) = - 3 2 - 1 2 ( x - 5 π 6 ) + 3 4 ( x - 5 π 6 ) 2 , T 00 3 ( x ) = - 1 2 + 3 2 ( x - 5 π 6 ), T 000 3 ( x ) = 3 2 . 3. (a) T 0 3 ( x ) = f 0 ( a ) + f 00 ( a )( x - a ) + f 000 ( a ) 2 ( x - a ) 2 , T 00 3 ( x ) = f 00 ( a ) + f 000 ( a )( x - a ), T 000 3 ( x ) = f 000 ( a ). 4. (a) T 2 ( x ) = ( x - 1) - 1 2 ( x - 1) 2 . (b) T 3 ( x ) = 1 + 1 2 x - 1 8 x 2 + 1 16 x 3 . (c) T 3 ( x ) = 3 2 + 1 2 ( x - π 3 ) - 3 4 ( x - π 3 ) 2 - 1 12 ( x - π 3 ) 3 . (d) T 4 ( x ) = - 1 + 1 2 ( x - π ) 2 - 1 24 ( x - π ) 4 . 5. T n ( x ) = n X k =0 x k 2 k +1 . 6. (a) | f (4) ( x ) | = ± ± ± ± - 15 16 (1 + x ) - 7 / 2 ± ± ± ± , (b) 3 . 9 × 10 - 6 , (c) | f (0 . 1) - T 3 (0 . 1) | = 3 . 65 × 10 - 6 . 7. (b) 1
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Unformatted text preview: . 7 10-4 . 8. (b) (0 . 1) n +2 ( n + 2)! , (c) n = 5, (d) sin(0 . 1) = 0 . 09983341665, T 5 (0 . 1) = 0 . 09983341667. 9. (d) diverges; the rest converge. 11. (c), (d), and (f) diverge; the rest converge....
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