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  • log x -tan^-1 x increases in the interval

log x -tan^-1 x increases in the interval

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Solution:   We have ,     f(x)=log_ex - an^-1 x

                  Rightarrow       fracmathrmd ymathrmd x=frac1x-frac11+x^2=frac1+x^2-xx(1+x^2)

                 Rightarrow                         =frac(x-frac12)^2+frac34x(1+x^2)> 0    forallbbbx> 0

                Hence ,   f(x)   is  an increasing function in the interval   (0,infty )

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Deependra Verma

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