Prove that the following functions are strictly increasing: `f(x)=log(1+x)-(2x)/(2+x)` for x > -1

Prove that the following functions are strictly increasing: f(x)=cot^(-1)x+x

Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

Show that the function f(x) = 2x+1 is strictly increasing on R.

Prove that the following functions do not have maxima or minima:(i) f (x) = e x (ii) g(x) = log x (iii) h(x)=x^3+x^2+x+1

Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

Prove that the function f(x)=(log)_e x is increasing on (0,\ oo) .

Show that the function f(x)=2x+3 is strictly increasing function on Rdot

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

Find for what values of x the following functions would be identical. f(x)=log(x-1)-log(x-2) and g(x)=log((x-1)/(x-2))