I am supposed to find this limit without L'Hopital's rule. I have tried multiplying the numerator and the denominator with (1/(1-x))+1, and I've looked for ways to factorize, without getting anywere. Would appreciate any help! =)

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- Jul 5th 2010, 01:28 PMgralla55limit problem
I am supposed to find this limit without L'Hopital's rule. I have tried multiplying the numerator and the denominator with (1/(1-x))+1, and I've looked for ways to factorize, without getting anywere. Would appreciate any help! =)

- Jul 5th 2010, 01:39 PMAlso sprach Zarathustra

so when the above equals to - Jul 5th 2010, 02:04 PMgralla55
Thank you very much! Would you mind explaining exactly how you simplified the limit? Did you just muliply the numerator and the denominator with (x+1)? I would never have spotted that, thanks again!

- Jul 5th 2010, 04:45 PMAlso sprach ZarathustraOf course...
- Jul 5th 2010, 05:05 PMAlso sprach Zarathustra
And something more...

I notice that you have posts already and yet you haven't try write math with Latex, I strongly recommend you to try it!

You can start learning this here, on this site there is a forum about Latex...

...but the best way I think is by double-clicking on the code, you can try it with my post above!

Anyway... good-luck!(Cool) - Jul 5th 2010, 08:38 PMtheodds
Another quick way to see this is to note that if then

by definition. Given the way the limit was set up, this is probably what was expected. - Jul 6th 2010, 03:43 PMgralla55
Thanks alot! I tried using Latex for this next problem, but I kept getting errors. I will have to start using it on easier expressions first I think... Anyway, in this problem, is it possible for me to go from step 2 to step 3 like I did here? In that case, the rest of the problem is easy.

- Jul 6th 2010, 03:49 PMtheodds
You can do this using the same trick I mentioned. If then

To get at the same thing you are suggesting here, note that you can rewrite the second expression as

Then take the limit, using the usual results for this types of things. - Jul 6th 2010, 03:56 PMgralla55
That will indeed work! I've never seen anyone using the defintion of the derivative in solving limit problems like that, haha. But if I do it like I did, then it will also simplify to 1 times cos (pi/6) which is what you got. I'm just not sure if I can rewrite it like that. It would be nice to know for future problems.

- Jul 6th 2010, 03:58 PMAlso sprach Zarathustra
- Jul 6th 2010, 04:00 PMtheodds
- Jul 6th 2010, 04:13 PMgralla55
Thank you both! Very helpful! Using the last limit properties, can I solve the problem like this?

- Jul 6th 2010, 04:19 PMAlso sprach Zarathustra
- Jul 6th 2010, 04:23 PMAlso sprach Zarathustra
- Jul 6th 2010, 04:30 PMtheodds
You can't move the limit taking into the denominator, because . The rule for moving limits around doesn't allow for this. The result would be undefined to begin with.

The limit results you want to use (taken as given) are: