How do you find lim as x approaches 0 of 3x/sin3x

Question

debbieg · Answer

hmm. Do you know L'Hospital's rule? I think that would work here...?

anonymous · Answer

not at L'Hospital's rule yet?

debbieg · Answer

bummer. Maybe you're supposed to do limit of the difference quotient?

debbieg · Answer

oh duh.... sorry, not DQ... limit as x->0.... forget the DQ.

debbieg · Answer

Welllll... I'm trying to figure out how to do it without L'hospital.... 

I think that rewriting the den'r sin(3x) using a trig ID should be part of it. I used sin(3x)=cos(pi/2 - 3x) and then you can expand that with the cosine of a difference. That makes the den'r non-zero... but the num'r is still 0, but I know that the limit is 1... having trouble getting that without l'hospital though.