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Pre-Calc Homework Solutions 372

# Pre-Calc Homework Solutions 372 - 372 dy dx dy dx dy dx...

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8. } d d y x } 5 } d d x } 3 ( 2 1) n } (2 x n 2 1 n 1 1 1)! } 4 5 ( 2 1) n } (2 (2 n n 1 1 1 1 ) x )! 2 n }5 } ( 2 (2 1 n ) n ) x ! 2 n } 9. } d d y x } 5 } d d x } } ( x ( 1 2 n a )! ) 2 n }5 } 2 n ( x ( 1 2 n a )! ) 2 n 2 1 }5 } ( ( 2 x n 1 2 a 1 ) 2 ) n ! } 10. } d d y x } 5 } d d x } } (1 2 n ! x ) n } 5 } n (1 2 x n ) n ! 2 1 ( 2 1) }52 } (1 ( n 2 2 x ) 1 n ) 2 ! 1 } Section 9.2 Exercises 1. Substitute 2 x for x in the Maclaurin series for sin x shown at the end of Section 9.2. sin 2 x 5 2 x 2 } (2 3 x ! ) 3 } 1 } (2 5 x ! ) 5 } 2 1 ( 2 1) n } ( ( 2 2 n x ) 1 2 n 1 1) 1 ! }1 5 2 x 2 } 4 3 x 3 } 1 } 4 1 x 5 5 } 2 1 } ( 2 ( 1 2 ) n n ( 1 2 x 1 ) 2 ) n ! 1 1 }1 This series converges for all real x . 2. Substitute 2 x for x in the Maclaurin series for ln (1 1 x ) shown at the end of Section 9.2. ln (1 2 x ) 5 ( 2 x ) 2 } ( 2 2 x ) 2 } 1 } ( 2 3 x ) 3 } 2 1 ( 2 1) n 2 1 } ( 2 n x ) n } 1 52 x 2 } x 2 2 } 2 } x 3 3 } 2 2 } x n n } 2 This series converges when
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