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

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)=secx-cos e cx ,x in (0,pi/2)

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

Prove that the function f(x)=x^(2)+2 is strictly increasing in the interval (2,7) and strictly decreasing in the interval (-2, 0).

The function sin^(4)x+cos^(4)x is increasing in the interval

Integrate the functions e^(x)sinx

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

Prove that the function f(x)=x-sinx is increasing on the real line . Also discuss for the existence of local extrema.

Prove that the functions do not have maxima or minima: f(x) = e^(x)