how to get it

RauLiTo · 2006-10-16 06:22:22

how to get this lim ?

polylog · 2006-10-16 07:23:04

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.

Dross · 2006-10-16 08:05:26

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.

polylog · 2006-10-16 08:17:19

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

Dross · 2006-10-16 08:28:43

RauLiTo · 2006-10-16 09:51:16

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

mikau · 2006-10-16 10:17:12

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

RauLiTo · 2006-10-16 10:21:29

its not from my book !

polylog · 2006-10-16 10:41:44

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 )

RauLiTo · 2006-10-16 10:43:27

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

RauLiTo · 2006-10-16 10:46:11

oh thank you alot polylog ...
there is no way to solve it without differbtiation ? i meant just with limits and continuity ?!

polylog · 2006-10-16 10:49:38

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

RauLiTo · 2006-10-16 10:53:12

thanks again !

Dross · 2006-10-16 10:55:22

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

Math Is Fun Forum

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

how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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

Re: how to get it

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