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

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

Show that the function given by f(x) = e^(2x) is strictly increasing on R.

Prove that every rational function is continuous.

Prove that the function given by f(x) = cos x is (b) strictly increasing in (pi,2 pi) .

Show that the function given by f(x) = 3x + 17 is strictly increasing on R.

Prove that the function f given by f(x) = log sin x is increasing on (0,(pi)/(2)) and decreasing on ((pi)/(2),pi) .

Show that the function given by f(x) = sin x is (a) strictly increasing in (0, (pi)/2) .

Find the interval in which the following functions are strictly increasing or decreasing. (b) 10 - 6x - 2x^(2)

Prove that the function given by f(x) = cos x is (a) strictly decreasing in (0, pi) .