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Unformatted text preview: 2 n sin n 2 + (-1) n n 2-1 n 2 cos n 2 cos nx- 2 n cos n 2 + 1 n 2 sin n 2 sin nx . 25. or (a) and (b), see plots. (c) We have s n ( x ) = n k =1 sin kx k . So s n (0) = 0 and s n (2 ) = 0 For all n . Also, lim x + f ( x ) = 2 , so the dierence between s n ( x ) and f ( x ) is equal to / 24 at x = 0. But even we look near x = 0, where the ourier series converges to f ( x ), the dierence | s n ( x )-f ( x ) | remains larger than a positive number, that is about . 28 and does not get smaller no matter how large n . In the fgure, we plot | f ( x )-s 150 ( x ) | ....
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.
- Fall '11