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  • The value of so that the function <img alt="\mathrm{f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x}}" src="/latex-image/?%5Cma

The value of \mathrm{f(0)} so that the function \mathrm{f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x}} is continuous at each point on its domain is
 

Option: 1

2

 


Option: 2

\frac{1}{3}


Option: 3

\frac{2}{3}


Option: 4

\frac{1}{3}


Answers (1)

best_answer

\mathrm{\lim _{x \rightarrow 0} f(x) =f(0) \quad \Rightarrow \quad \lim _{x \rightarrow 0} \frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} }

\mathrm{ =\lim _{x \rightarrow 0} \frac{2-\frac{\sin ^{-1} x}{x}}{2+\frac{\tan ^{-1} x}{x}}=\frac{2-1}{2+1}=\frac{1}{3} \quad \therefore \quad f(0)=\frac{1}{3} }

Hence option 2 is correct.
 

Posted by

Rakesh

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