Pre-Calc Homework Solutions 375

Pre-Calc Homework Solutions 375 - Section 9.2 22(a a0 a1 a2...

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22. (a) a 0 5 1 a 1 5 } 3 1 } a 0 5 3 ? 1 5 3 a 2 5 } 3 2 } a 1 5 } 3 2 } ? 3 5 } 9 2 } a 3 5 } 3 3 } a 2 5 a 2 5 } 9 2 } Since each term is obtained by multiplying the previous term by } 3 n } , a n 5 } 3 n n ! } . n 5 0 a n x n 5 1 1 3 x 1 } 9 2 } x 2 1 } 9 2 } x 3 1 1 } 3 n n ! } x n 1 (b) Since the series can be written as n 5 0 } (3 n x ! ) n } , it represents the function f ( x ) 5 e 3 x . (c) f 9 (1) 5 3 e 3 x ) x 5 1 5 3 e 3 23. First, note that cos 18 < 0.6603. Using cos x 5 n 5 0 ( 2 1) n } (2 x n 2 n )! } , enter the following two-step commands on your home screen and continue to hit ENTER. The sum corresponding to N 5 25 is about 0.6582 (not withing 0.001 of exact value), and the sum corresponding to N 5 26 is about 0.6606, which is within 0.001 of the exact value. Since we began with N 5 0, it takes a total of 27 terms (or, up to and including the 52nd degree term). 24.
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