lim x --> 0 ((1-cos x)/ x^2)

How would I go about calculating this limit?

Thankyou

Printable View

- Nov 1st 2010, 03:36 AMkatedew987Calculating a Limit
lim x --> 0 ((1-cos x)/ x^2)

How would I go about calculating this limit?

Thankyou - Nov 1st 2010, 03:48 AMUnknown008
Maybe you can use the l'Hopital's rule twice.

That is, you differentiate the numerator and denominator with respect to x twice. - Nov 1st 2010, 03:51 AMkatedew987
Unfortunately, we're not yet allowed to use that rule. At this stage we're only supposed to be assuming that lim x--> sin x/ x = 1 and lim x--> 0 (1- cos x)/ x = 0. Thankyou for the input anyway though!

- Nov 1st 2010, 05:03 AMharish21
- Nov 1st 2010, 05:06 AMkatedew987
No, sorry, perhaps I didn't make it clear enough, I'm supposed to be finding lim x--> 0 ((1-cosx)/ x^2) working on the assumption that lim x--> (1 - cos x) = 0

- Nov 1st 2010, 01:53 PMhjortur
How did you do the original proof that

? - Nov 1st 2010, 02:02 PMAlso sprach Zarathustra
Use

And use:

YOU will get that the limit is 1/2 - Nov 1st 2010, 02:08 PMDrexel28
- Nov 1st 2010, 02:16 PMchisigma