Prove that `f(x)=x-sinx` is an increasing function.

Prove that f(x)=x^(3) in an increasing function

Let f be a function defined on [a,b] such that f'(x)>0 for all quad x in(a,b) ( Then prove that f is an increasing function on (a,b).

f(x) = e^(sinx+cosx) is an increasing function in

Prove the following (i) f(x)=sinx is : (I) strictly increasing in (0, (pi)/(2)) (II) strictly decreasing in ((pi)/(2), pi) (III) neither increasing nor decreasing in (0, pi) (ii) f(x)=2sinx+1 is an increasing function on [0, (pi)/(2)].

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in

Prove that f (x) = e^(3x) is strictly increasing function on R.

Find the interval for which f(x)=x-sinx is increasing or decreasing.

Show that f(x) = (x)/(sinx) is increasing on [0, (pi)/(2)]

Let f be the function f(x)=cos x-(1-(x^(2))/(2))* Then f(x) is an increasing function in (0,oo)f(x) is a decreasing function in (-oo,oo)f(x) is an increasing function in (-oo,oo)f(x) is a decreasing function in (-oo,0)