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sol11-1

sol11-1 - Chapter 11 Exercises 11.1 1 p3 x = sin 0 cos(0 x...

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357 Chapter 11 Exercises 11.1 1. p 3 ( x ) = sin0 + cos(0) x + sin0 2! x 2 + cos0 3! x 3 = x 1 6 x 3 2. p 3 ( x ) = e 0/2 1 2 e 0/ 2 x + 1 4 e 0/2 x 2 2! 1 8 e 0/ 2 x 3 3! = 1 1 2 x + 1 8 x 2 1 48 x 3 3. p 3 ( x ) = 5 e 2(0) + 10 e 2(0) x + 20 e 2(0) x 2 2! + 40 e 2(0) x 3 3! = 5 + 10 x + 10 x 2 + 20 3 x 3 4. p 3 ( x ) = cos π + (5sin π ) x (25cos π ) x 2 2! (125sin π ) x 3 3! = − 1 + 25 2 x 2 5. p 3 ( x ) = 1 + 2 x 4 x 2 2! + 24 x 3 3! = 1 + 2 x 2 x 2 + 4 x 3 6. p 3 ( x ) = 1 2 1 2 2 x + 2 2 3 x 2 2! 6 2 4 x 3 3! = 1 2 1 4 x + x 2 8 x 3 16 7. f ( x ) = xe 3 x ; f ( x ) = e 3 x + 3 xe 3 x f ( x ) = 3 e 3 x + 3 e 3 x + 9 xe 3 x = 6 e 3 x + 9 xe 3 x f ( x ) = 18 e 3 x + 9 e 3 x + 27 xe 3 x = 27 e 3 x + 27 xe 3 x p 3 ( x ) = 0 + (1 + 0) x + (6 + 0) x 2 2! + (27 + 0) x 3 3! = x + 3 x 2 + 9 2 x 3 8. p 3 ( x ) = 1 1 2 x 1 4 x 2 2! 3 8 x 3 3! = 1 1 2 x 1 8 x 2 1 16 x 3 9. p 4 ( x ) = e 0 + e 0 x + e 0 x 2 2! + e 0 x 3 3! + e 0 x 4 4! = 1 + x + x 2 2 + x 3 6 + x 4 24 e .01 1 + .01 + (.01) 2 2 + (.01) 3 6 + (.01) 4 24 = 1.01005 10. f ( x ) = ln(1 – x ); f ( x ) = − 1 (1 x ) ; f ( x ) = − 1 (1 x ) 2 ; f ( x ) = − 2 (1 x ) 3 ; f (4) ( x ) = − 6 (1 x ) 4 p 4 ( x ) = 0 x x 2 2! 2 x 3 3! 6 x 4 4! = − x 1 2 x 2 1 3 x 3 1 4 x 4 ln(.9) = ln(1 – .1) –.1 (.1) 2 2 (.1) 3 3 (.1) 4 4 = − .10536

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