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January 11th, 2013, 02:06 PM   #1
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simplification of a limit

Hi,

I've a problem with the semplification of a limit..

My limit is:



I know the result because I used wolframalpha :P

then, I've think to divide this limit in this way:



I've divided the fraction and I've used the properties of limits..

There is:



So I've think to omit it and rewrite:



but:



I think that I can't resolve only x/sinx.. why? Can someone explain me the invalid passage please?

Thanks!
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January 11th, 2013, 03:45 PM   #2
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Re: simplification of a limit

Hello, elviro!

Quote:

If you are allowed L'Hopital's rule, apply it twice.

soroban is offline  
January 12th, 2013, 02:06 AM   #3
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Re: simplification of a limit

yes, but I don't understand why my method isn't right
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January 12th, 2013, 12:29 PM   #4
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Re: simplification of a limit

Quote:
Originally Posted by elviro
yes, but I don't understand why my method isn't right
The x/sinx term can't simply be repalced by 1. You need to include the next term in the expansion (x^2/6) when taking the limit.
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