Finding $\lim\limits_{x\to 0}\frac{\sin{3x}}{x}$ I am trying to find the limit of 
$$\lim_{x\to 0}\frac{\sin{3x}}{x}$$
I have no idea what I am supposed to do. I know the identity that,
$$\lim_{x\to0}\frac{\sin{x}}{x} = 1$$
but that will not be good enough on a test and I am not sure why that is true anyways. I do not know how I am supposed to proceed with this problem. 

Hint: $\dfrac{\sin 3x}{x}=3\dfrac{\sin 3x}{3x}$
