If the function f(x)= 2x- ^ -1 x 2x+ ^ -1 x is continuous at each… - Vidyadip

Question

If the function $\text{f(x)}=\frac{2\text{x}-\sin^{-1}\text{x}}{2\text{x}+\tan^{-1}\text{x}}$ is continuous at each point of its domain, then the value of f(0) is:

$2$
$\frac{1}{3}$
$-\frac{1}{3}$
$\frac{2}{3}$

✓

Answer

$\frac{1}{3}$

Solution:
$\text{f}(0)=\lim\limits_{\text{x}\rightarrow0}\frac{2\times-\sin^{-1}\text{x}}{2\times+\tan^{-1}\text{x}}$
$\text{f}\text{(0)}=\lim\limits_{\text{x}\rightarrow0}\frac{2\times-\frac{\sin^{-1}\text{x}}{\text{x}}}{2+\frac{\tan^{-1}\text{x}}{\text{x}}}$
$\text{f}(0)=\frac{2-1}{2+1}=\frac{1}{3}$

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