Is my approach to finding the limit of trig functions correct?

[jkristia]

I'm still trying to figure out how to do limits of trig functions and I would like to know if this is the correct approach. I know the answer is correct, but not sure if that is just a coincidence.

Homework Statement

lim (x -> 0) of (sin 2x) / (sin3x).

Homework Equations

The Attempt at a Solution

First I try to get the equation into the form (sin x) / x or x / (sin x)
so I multiply by

(x/x)(3/3)(2/2)

this gives me

(1/3)(3x/sin3x)(2/1)(sin2x/2x)

so I get
(1/3)(1)(2/1)(1) = 2/3

Is that the correct approach?

 

[Infinitum]

Yes, it is

Edit : Another way to solve this would be the use of L'Hospital principle, but this method is more elegant, in my opinion.

 

[jkristia]

Thank you very much for the quick reply.

I'm trying to do calculus as a selfstudy, and the L'Hospital is not mentioned until another 320 pages.