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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

how to get this lim ?

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**polylog****Member**- Registered: 2006-09-28
- Posts: 162

It looks like you can use L'Hopital's rule twice; the denominator will be reduced to 2x, then to 2. At that point setting x = 1 in the expression will produce a finite value.

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**Dross****Member**- Registered: 2006-08-24
- Posts: 325

polylog wrote:

It looks like you can use L'Hopital's rule twice; the denominator will be reduced to 2x, then to 2. At that point setting x = 1 in the expression will produce a finite value.

You can use L'Hopital once, but after that the denominator will be 2x. It now doesn't equal zero when x equals one. You might be able to do some rearranging, though.

Bad speling makes me [sic]

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**polylog****Member**- Registered: 2006-09-28
- Posts: 162

Oh yes, indeed, the rule can only be applied once. Then x can be set to 1.

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**Dross****Member**- Registered: 2006-08-24
- Posts: 325

Bad speling makes me [sic]

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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

thanks alot guys ... but can you tell me what is this rule '' L'Hopital's rule '' ? maybe i learnt it but i dont know what do they call it in english ... i want more explaination please

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

WHAT? Your book asked you this and it didn't teach you L' Hoptials rule?

A logarithm is just a misspelled algorithm.

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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

its not from my book !

ImPo$$!BLe = NoTH!nG

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**polylog****Member**- Registered: 2006-09-28
- Posts: 162

Actually in my first year calculus course they also gave us limit questions which required L'Hopital's rule but which was not taught yet; I suppose there is some weird other way of doing it but this is the best way!

So here is L'Hopital's Rule for the case of rational functions:

Consider a limit

If f(a)/g(a) gives an *indeterminate form*, such as:

Then you are allowed to differentiate the top and bottom functions:

If this new limit also gives an indeterminate form, you can differentiate the top and bottom again until the quotient gives a 'normal' value.

(The actual definition is more technical and precise, but I think this is sufficient for school assignments )

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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

i saw it in my book ! we didnt learn that lesson yet !!!

thank you everybody

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

oh thank you alot polylog ...

there is no way to solve it without differbtiation ? i meant just with limits and continuity ?!

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**polylog****Member**- Registered: 2006-09-28
- Posts: 162

There might be, but it's more difficult... I can't think of a way to do it without differentiation.

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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

thanks again !

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**Dross****Member**- Registered: 2006-08-24
- Posts: 325

You could always derive L'Hopital's rule from first principles as part of the question. Or guess the answer and use a delta/epsilon proof to show it's correct

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