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If f(x)=tan^(-1)x,g(x)=tan^(-1)((1+x)/(1...

If `f(x)=tan^(-1)x,g(x)=tan^(-1)((1+x)/(1-x))" for "|x|lt1`, show that `f'(x)=g'(x)andg(x)-f(x)=pi/4`.

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Knowledge Check

  • If f(x)=x*tan^(-1)x," then: "f'(1)=

    A
    `(pi)/(4)+(1)/(2)`
    B
    `(pi)/(4)-(1)/(2)`
    C
    `(1)/(2)-(pi)/(4)`
    D
    `-(pi)/(8)`

  • If : f(x)=x*tan^(-1)x," then: "f'(1)=

    A
    `1+(pi)/(4)`
    B
    `(1)/(2)+(pi)/(4)`
    C
    `(1)/(2)-(pi)/(4)`
    D
    2

  • Let f(x) = tan^(-1) x and g(x) = (x)/(1 + x^(2)), x gt 0 then

    A
    `f(x) lt g (x), " on "(0, oo)`
    B
    `f(x) le g (x) " on "[1, oo)`
    C
    `g (x) lt f(x) " on "(0, oo)`
    D
    none of these

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    tan^(-1)((1+x)/(1-x))=(pi)/(4)+tan^(-1)x,x<1

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