Solve the limit algebraically. No L'Hôpital's Rule.
\(\lim_{x\rightarrow 0} \frac{3sin(4x)}{sin(3x)}\)
As x→0 sin(ax)→ax, so \(\lim_{x\rightarrow 0}\frac{3sin{4x}}{sin{3x}}\rightarrow\frac{3*4x}{3x}\rightarrow4\)