I need to find Lim (x->0) arcsin(2x)/arcsin(3x) by substitution

1. Nov 8, 2008

Petkovsky

I need to find Lim (x->0) arcsin(2x)/arcsin(3x)

I can do a substitution
arcsin(2x) = y => 2x = sin(y)

and get arcsin(sin(y)) for the nominator, which is equal to y.
However, for the denominator i get arcsin(3/2 sin(y)) which I'm not sure what to do with.

Am I on the right path?

2. Nov 8, 2008

gabbagabbahey

Re: Limits

Since arcsin(0)=0, you have a limit of the form 0/0...so why not use L'hopital's rule?

3. Nov 8, 2008

Petkovsky

Re: Limits

Well unfortunatelly i can't even tough i know it, because we haven't covered that part yet.