Question

The value of $f\left(0\right)$ so that the function $f\left(x\right)=\frac{2x-{\sin }^{-1}x}{2x+{\tan }^{-1}x}$ is continuous at
each point in its domain, is equal to

• A. $2$
• B. $\frac{1}{3}$.
• C. $\frac{2}{3}$.
• D. $\frac{-1}{3}$.

Answer 1

Answer: (B)

$\frac{1}{3}$.

$\underset{x\to 0}{lim}{\text{sin}}^{-1}x=x;\underset{x\to 0}{lim}{\text{tan}}^{-1}x=x$

$\underset{x\to 0}{lim}\frac{2x-{\text{sin}}^{-1}x}{2x+{\text{tan}}^{-1}x}=\underset{x\to 0}{lim}\frac{2x-x}{2x+x}=\frac{1}{3}$

So to be continuous it should be $\frac{1}{3}$.