# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2006-10-16 06:22:22

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

### how to get it

how to get this lim ?

ImPo\$\$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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## #2 2006-10-16 07:23:04

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

### Re: how to get it

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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## #3 2006-10-16 08:05:26

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

### Re: how to get it

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.

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## #4 2006-10-16 08:17:19

polylog
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Registered: 2006-09-28
Posts: 162

### Re: how to get it

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

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## #5 2006-10-16 08:28:43

Dross
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Registered: 2006-08-24
Posts: 325

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## #6 2006-10-16 09:51:16

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

### Re: how to get it

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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## #7 2006-10-16 10:17:12

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

### Re: how to get it

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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## #8 2006-10-16 10:21:29

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

### Re: how to get it

its not from my book !

ImPo\$\$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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## #9 2006-10-16 10:41:44

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

### Re: how to get it

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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## #10 2006-10-16 10:43:27

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

### Re: how to get it

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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## #11 2006-10-16 10:46:11

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

### Re: how to get it

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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## #12 2006-10-16 10:49:38

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

### Re: how to get it

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

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## #13 2006-10-16 10:53:12

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

### Re: how to get it

thanks again !

ImPo\$\$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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## #14 2006-10-16 10:55:22

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

### Re: how to get it

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