Thursday, 13 December 2012

Find the limit as n approaches infinite



We have the following function:



Un=sin13nπ



What is the limit of this function as n approaches infinity?




I first tried to use my calculator as help, for n I chose some arbitrary large numbers, such as 100 and 1000. Then I I just took n=1050 and it gave me an error.



So the correct answer is it doesn't have one, but why? Why does this function have a solution for n=102,103 and not for bigger numbers such as n=1050?


Answer



As David hinted in his comment, try using the fact that
sin(x+2πk)=sin(x)
whenever k is an integer. Or, if you just write out the first few values of Un (compute these using the unit circle) and you should notice a pattern.



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