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Prove that ln (1+1/x) gt (1)/(1+x), x g...

Prove that `ln (1+1/x) gt (1)/(1+x), x gt 0`. Hence, show that the function `f(x)=(1+1/x)^(x)` strictly increases in `(0, oo)`.

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(log x)^(log x),x gt1

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