Limit of lim (x->0) of the following maclaurin/taylor problem

[Riazy]

Homework Statement

Calculate the lim x--> 0 ( 1/sinx - 1/ln(1+x))

I have a problem understanding what to do with the O notations (ordos in latin) Are there specific rules for them? What are these rules then?

Homework Equations

It's the same as ln(1+x) - sinx / sinx * ln(1+x)

The Attempt at a Solution

= this gives us = lim x--> 0 = x-x^2/2 - x + Ô(x^3) / (x-x^2/2 + O(x^3) *(x +O(x^3))

With my limited knowledge of ordo at all + that we don't have much detailed information
but examples in our book, I can't say that I have grasped much of the subject, I must
admit that I think it's a hard subject for me

If i look at the first expression x-x^2/2 I have developed it this far because I want something in the numerator and the denominator to cancel,

I don't know what to do from here in order to complete the problem, could someone help?-.

 

[Gib Z]

Here is a good resource to help you with the notation and ideas: http://www.artofproblemsolving.com/Forum/download/file.php?id=1412

I would suggest leaving this specific problem for now, reading that pdf and going through all of its basic examples first, before trying this again.

 

[Riazy]

The website takes me to a blank page, is it the full address?

 

[Gib Z]

Yes it is. If it doesn't work, you might have to make an account on that website to see it, but it's quite quick and well worth it.