Prove that `ln(1 + x)>(tan^(- 1)x)/(1+x), x >0`

Prove that ln(1+x) 0.

Prove that ln(1+x) 0.

Prove that ln(1+x) 0.

log(tan^(-1)x)

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) .

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) .

e^(tan^(-1)x)log(tan x)

Prove that ln(1+x)

Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0, -pi/2 if x<0

Prove that (x)/(1+x)>ln(1+x) 0