Question

Solve:$\underset{x\to 0}{lim}\frac{{\tan }^{-1}x}{x}.$ solve.

Answer 1

${lim}_{x⟶0}\frac{{\tan }^{-1}x}{x}putx=\tan \theta whenx⟶0,\theta ⟶0\therefore {lim}_{x⟶0}\frac{{\tan }^{-1}x}{x}={lim}_{\theta ⟶0}\frac{\theta }{\tan \theta }={lim}_{\theta ⟶0}\frac{1}{\frac{\tan \theta }{\theta }}=\frac{1}{{lim}_{\theta ⟶0}\frac{\tan \theta }{\theta }}(\because {lim}_{x⟶0}\frac{\tan x}{x})$