Pre-Calc Homework Solutions 373

Pre calc homework solutions 373

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Unformatted text preview: Section 9.2 8. Substitute 2x for x in the Maclaurin series for e x shown at x1/2 373 12. f(4) f (4) f (4) f (4) P0(x) x 4 2 1 4 f (4) 1 , so 2! 32 f (4) 3 , so 3! 256 1 512 1 64 the end of Section 9.2. e 2x 1 2x ( 2x) 2x 2 1 ( 2x)2 ... 2! n n n ... ( 1) 2 x n! ( 2x)n n! ... 1 1/2 x 2 x 4 1 3/2 x 4 x 4 3 5/2 x 8 x 4 ... The series converges for all real x. 9. f (2) f (2) f (2) f (2) P0(x) P1(x) P2(x) P3(x) 10. f f f 4 4 4 1 2 1 2 1 2 1 2 1 xx 2 1 2 2 x 2 3 2 2 2 2 x 4 x 4 x 4 4 4 4 (x 4)2 64 (x 4)2 64 x 2x 1 4 1 x 2 4 4 6x x 2 , so f (2) 1 2! 8 3 f (2) , so 8 3!...
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