1. Tardigrade
  2. Question
  3. Mathematics
  4. Find the value of f(0), so that the function f(x)=(2 x- sin -1 x/2 x+ tan -1 x) is continuous at each point in its domain.

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

Continuity and Differentiability

Solution:

$f(0)=\displaystyle\lim _{x \rightarrow 0} \frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x}, \frac{0}{0}$
$=\displaystyle\lim _{x \rightarrow 0} \frac{2-\frac{1}{\sqrt{1-x^{2}}}}{2+\frac{1}{1+x^{2}}}=\frac{1}{3}$