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If the function f9x)=(2x-sin^(-1)x)/(2x+...

If the function `f9x)=(2x-sin^(-1)x)/(2x+tan^(-1)x)` is continuous at each point of its domain, then the value of `f(0)` 2 (b) `1/3` (c) `-1/3` (d) `2/3`

A

`-(1)/(3)`

B

`(1)/(2)`

C

`(2)/(3)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`f(0)=underset(xto0)lim(2x-sin^(-1)x)/(2x+tan^(-1)x)`
`=underset(xto0)lim(2-(sin^(-1)x)/(x))/(2+(tan^(-1)x)/(x))=(2-1)/(2+1)=(1)/(3)`
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