I know that csc is 1/sin.
Would i do 3/6(1/sin)(3x)?
Please show me the correct steps if i'm wrong. Wouldn't it just be 0/0 and become DNE?
Rewrite:
$\displaystyle \lim_{x\to 0} \frac{3}{6x\csc(3x)}=\lim_{x\to 0} \frac{3}{\frac{6x}{\sin(3x)}}=\lim_{x\to 0}\frac{3\sin(3x)}{6x}$
Use the fact:
$\displaystyle \lim_{x\to 0} \frac{\sin(x)}{x}=1$
And yes $\displaystyle \frac{3}{2}$ is correct.