Without using series expansion of and binomial expansion of evaluate the limit :

Also,you cannot use the L'Hospital rule.

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- Sep 25th 2008, 06:19 AMpankajLimits without use of L'Hospital and series expansion
Without using series expansion of and binomial expansion of evaluate the limit :

Also,you cannot use the L'Hospital rule. - Sep 26th 2008, 05:08 PMChris L T521
Its not that we don't want to solve it...its just that we can't think of a clever way to do it! We're discussing that same limit here.

--Chris - Sep 27th 2008, 06:55 AMpankaj
Thanks Chris.I am myself on it.

- Sep 27th 2008, 08:49 AMCaptainBlack
The rules do not prevent you from using a series expansion of:

Or avoiding series the fact that and the definition of (3rd) derivative to give:

(here denotes a function such that the limit as goes to of this function divided by goes to zero) which will allow the evaluation of the limit.

I suspect though that you might consider all this to be cheating as this is tantamount to either L'Hopital's rule and/or the use of series)

RonL - Oct 14th 2008, 04:26 PMpankaj
Please check my solution

The limit does not change if x is replaced by -x

i.e.

Putting

- Oct 14th 2008, 08:18 PMCaptainBlack
- Oct 15th 2008, 06:12 AMpankaj
I thought it was a standard formula or a definition

- Oct 15th 2008, 06:41 AMChop Suey
- Oct 15th 2008, 08:46 AMCaptainBlack
- Oct 15th 2008, 09:29 AMKrizalid
Well, there's a way to justify the value of that limit. Try to find it.

- Oct 15th 2008, 11:35 AMCaptainBlack
- Oct 15th 2008, 11:38 AMKrizalid
Haha, yeah, sorry, I misexpressed myself. I actually mean, a substitution method that's all.