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 Post subject: monotonocity problem
PostPosted: Wed, 16 May 2012 18:04:16 UTC 
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discuss the monotonocity of sin\frac{\pi}{x} on R
i am getting the interval but how to check on each and every interval.

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 Post subject: Re: monotonocity problem
PostPosted: Wed, 16 May 2012 22:53:41 UTC 
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mun wrote:
discuss the monotonocity of sin\frac{\pi}{x} on R
i am getting the interval but how to check on each and every interval.

What is it you want to check? The interval ends are at odd multiples of π/2, i.e. 1/x is an odd multiple of 1/2.


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 Post subject: Re: monotonocity problem
PostPosted: Wed, 16 May 2012 23:15:22 UTC 
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mun wrote:
discuss the monotonocity of sin\frac{\pi}{x} on R
i am getting the interval but how to check on each and every interval.


The derivative is -{\pi\over x^2}\cos{\pi\over x}, for it to change sign you need that \cos{\pi\over x} has the same sign on an entire interval, so use what you know about zeros of the cosine function to finish the problem.

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