$\underset{x→0}{\lim}(\frac{x}{\tan^{-1}2x})$ is equal to

0 $\frac{1}{2}$ 1 ∞

$\frac{1}{2}$

Let $\tan^{-1}2x=θ⇒x=\frac{1}{2}\tan θ$ and x → 0, θ → 0 $⇒\underset{x→0}{\lim}\frac{x}{\tan^{-1}2x}=\underset{θ→0}{\lim}\frac{\frac{1}{2}\tan θ}{θ}=\frac{1}{2}$