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

Which of the following functions is increasing in (0 , oo) ?

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

Prove that the function are increasing for the given intervals: f(x)=secx-cos e cx ,x in (0,pi/2)

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)=e^x+sinx ,x in R^+

Prove that the function f(x)=x^(2)-2x-3 is strictly increasing in (2, infty)

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.