hw01_sol - % % % % % HW 2 Problem 9 To c h e c k t h a t s...

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Unformatted text preview: % % % % % HW 2 Problem 9 To c h e c k t h a t s i n ( ( 2 n −1)/n ˆ3) = O ( 1/nˆ2 ) we go b a c k t o t h e d e f i n i t i o n and c h e c k n u m e r i c a l l y w h e t h e r s i n ( ( 2 n −1)/n ˆ3) / (1/ n ˆ2) i s bounded by a c o n s t a n t . This i s t h e c a s e as t h e c u r v e b e l o w i s l e s s than 2 . n = 10:2000; plot ( n , n . ˆ 2 . ∗ sin ( ( 2 ∗ n −1) . / n . ˆ 3 ) ) ; xlabel ( ’ n ’ ) ; ylabel ( ’ | x n | / | \ a l p h a n | ’ ) 2 1.98 1.96 |xn|/|αn| 1.94 1.92 1.9 1.88 0 500 1000 n 1500 2000 ...
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This note was uploaded on 01/04/2011 for the course MATH 4610 taught by Professor To during the Spring '10 term at SUNY Geneseo.

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