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 Post subject: limitPosted: Tue, 28 Sep 2010 13:13:28 UTC
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[ (1+x)^(1/x) -e-(e)( x)/2]/x^2
limit x---0

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 Post subject: Re: limitPosted: Tue, 28 Sep 2010 15:20:50 UTC
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mun wrote:
[ (1+x)^(1/x) -e-(e)( x)/2]/x^2
limit x---0

The limit does not exist.

Perhaps you mean ?

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 Post subject: Re: limitPosted: Tue, 28 Sep 2010 16:35:22 UTC
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outermeasure wrote:
mun wrote:
[ (1+x)^(1/x) -e-(e)( x)/2]/x^2
limit x---0

The limit does not exist.

Perhaps you mean ?[/quote
yes sir your answer is right but how

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 Post subject: Re: limitPosted: Tue, 28 Sep 2010 16:44:17 UTC
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mun wrote:
outermeasure wrote:
mun wrote:
[ (1+x)^(1/x) -e-(e)( x)/2]/x^2
limit x---0

The limit does not exist.

Perhaps you mean ?

yes sir your answer is right but how

Taylor expand about x=0.

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 Post subject: Re: limitPosted: Tue, 28 Sep 2010 17:11:06 UTC
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sir can we do this question without using taylor expansion.

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 Post subject: Re: limitPosted: Tue, 28 Sep 2010 23:05:05 UTC
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mun wrote:
sir can we do this question without using taylor expansion.

Maybe, but I can promise the work would be very ugly!
I think you should stick to Outermeasure's suggestion...you should know how to Taylor expand the exponential function!!

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 Post subject: Re: limitPosted: Wed, 29 Sep 2010 04:56:29 UTC
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mun wrote:
sir can we do this question without using taylor expansion.

You can. Justify why is sufficiently smooth and hence find the second derivative of at x=0. Now use Cauchy MVT.

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 Post subject: Re: limitPosted: Fri, 18 May 2012 15:36:51 UTC
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outermeasure wrote:
mun wrote:
sir can we do this question without using taylor expansion.

You can. Justify why is sufficiently smooth and hence find the second derivative of at x=0. Now use Cauchy MVT.

sir can you explain it further more as i don't know how to apply this theorem on limits.

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 Post subject: Re: limitPosted: Fri, 18 May 2012 16:39:32 UTC
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Using outermeasure Hint

First We will find expansion of at

Let

Taking on both side, We Get

Now We Calculate Limit

Using Expansion of

So

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 Post subject: Re: limitPosted: Fri, 18 May 2012 16:41:06 UTC
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To Outermeasure

Justify why is sufficiently smooth and hence find the second derivative of at x=0. Now use Cauchy MVT.[/quote]

sir can you explain it further more as i don't know how to apply this theorem on limits.[/quote]

I did not understand the above (2) line.

Thanks

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