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f(x)=cot^(-1)((2x)/(1-x^(2))), g(x)=cos^...

`f(x)=cot^(-1)((2x)/(1-x^(2))), g(x)=cos^(-1)((1-x^(2))/(1+x^(2)))` then `lim_(x to a)(f(x)-f(a))/(g(x)-g(a)), a in (0, (1)/(2))`

A

1

B

`-1`

C

2

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`cos^(-1)((1-x^(2))/(1+x^(2)))=2 tan^(-1)x`
`cos^(-1)((2x)/(1-x^(2)))=(pi)/(2)-tan^(-1)((2x)/(1-x^(2)))=(pi)/(2)-2 tan^(-1)x`
`lim_(x to a)(f(x)-f(a))/(g(x)-g(a))`
`lim_(x to a)(f'(x))/(g'(x))=-1`
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