a. $\lim_{x\to 0} \dfrac{\sin 3x}{3x} . \dfrac{2x}{\sin 2x} .\dfrac{2}{3}=\dfrac{2}{3}$
b. $\lim_{x\to 0}\dfrac{\tan 2x}{\sin 5x} =\lim_{x\to 0} \dfrac{1}{\cos 2x} .\dfrac{\sin 2x}{\sin 5x} =\lim_{x\to 0} \dfrac{1}{\cos 2x} \dfrac{\sin 2x}{2x} . \dfrac{5x}{\sin 5x} .\dfrac{5}{2}=\dfrac{5}{2}$
Lưu ý $\lim_{x\to 0}\dfrac{\sin ax}{ax}= 1 =\lim_{x\to 0}\dfrac{ax}{\sin ax}$