Is this the correct way to solve for the limit?
I found the limit $x\to 0$ of $\sin4x/ \tan7x$ by these steps
1) $\dfrac{\sin4x}{1} \cdot \dfrac{\cos7x}{\sin7x}$
2) I crossed out the $\sin x$ in the numerator and denominator leaving me with $\dfrac{4\cos7x}{7}$
3) $4 (\cos7(0)) = 4 (\cos0=1)$
4) I was left with $ 4/7$