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

Prove that the following functions are strictly increasing. f(x) = log (1 + x) - (2x)/(2 + x)

Prove that the logarithmic function is strictly increasing on (0,oo)

Find the intervals in which the following functions are strictly increasing or decreasing: 6-9x-x^2

Find the intervals in which the following functions are strictly increasing or decreasing: 10-6x-2x^2

Examine the following functions for continuity f(x)=1/(x-5)

Show that the function x^3-3x^2+6x-5 is strictly increasing on R.

Show that the function x^3-6x^2+15x+4 is strictly increasing in R.

Find the range of f(x) = cot^(-1)(2x - x^2)

Find the values of x of which the following functions are identical. f(x) = x and g(x) =1/(1//x)

Prove that the function f(x)=logsinx is strictly increasing in (0,pi/2) and strictly decreasing in (pi/2,pi)