QuestionFind the limit: $\lim _{x \rightarrow 0} \frac{\tan (2 x)}{3 x}=$ (A) $\frac{1}{3}$ (B) $\frac{1}{2}$ (C) $\frac{2}{3}$ (D) 2

Studdy Solution
As $x$ approaches0, $\tan(2x)$ also approaches0. So, the limit simplifies to$$\lim{x \rightarrow0} \frac{2(1 +0)}{3} = \frac{2}{3}$$So, the value of the limit $\lim{x \rightarrow0} \frac{\tan (2 x)}{3 x}$ is $\frac{2}{3}$.
Therefore, the correct answer is (C) $\frac{2}{3}$.