Prove that the function are increasing for the given intervals: `f(x)=sinx+tanx-2x ,x in (0,pi/2)`

Prove that the function are increasing for the given intervals: f(x)=sec x-csc x,x in(0,(pi)/(2))

Prove that the function are increasing for the given intervals: f(x)=e^(x)+sin x,x in R^(+)

Prove that the following functions are increasing for the given intervals, (i) y =e^(x) + sinx, x epsilon R^(+) (ii) y=sin x+ tan x- 2x, x epsilon(0, pi/2) (iii) y = x + sin x , x epsilon R .

The function f(x) = x^2 is increasing in the interval

The function f(x)=x^(2)+2x-5 is increasing in the interval

The function f(x)=(sinx)/(x) is decreasing in the interval

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sin^(2) x in the interval [0,pi] .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sin 3x in the interval [0,pi] .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sinx + cos x in the interval [0 , pi//2] .