Using monotonicity prove that
`x lt - ln (1-x) lt x (1-x)^(-1)` for `0 lt x lt 1`

Using monotonicity prove that (x)/(1-x^(2)) lt tan^(-1)x lt x for every x ge 0

Prove that (x)/((1 + x)) lt log (1 + x) lt x " for " x gt 0

Prove that (x)/(1 + x) lt log (1 + x) lt "x for x" gt 0

0 lt |x-1|lt3

Prove that tan (sin^(-1)x) = x/(sqrt(1-x^(2))) - 1 lt x lt 1 .

prove that (x)/(1+x) lt log (1+x)ltx , for all xgt 0

prove that (x)/(1+x) lt log (1+x)ltx , for all xgt 0

Function f(x) = |x| - |x - 1| is monotonically increasing when a) x lt 0 b) x gt 1 c) x lt 1 d) 0 lt x lt 1

y = cos^(-1)((1-x^2)/(1+x^2)), 0 lt x lt 1 .