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)

Find the values of x for which the following pair of functions are identical. (i) f(x)=tan^(-1)x+cot^(-1)x " and " g(x)=sin^(-1)x +cos^(-1)x (ii) f(x)=cos(cos^(-1)x) " and " g(x)=cos^(-1)(cosx)

Find the intervals in which the functions are strictly increasing or decreasing: (x+1)^(3) (x-3)^(3)

Find the intervals in which the functions are strictly increasing or decreasing: x^(2) +2x-5

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

Find the intervals in which the functions are strictly increasing or decreasing: -2x^(3)-9x^(2) -12x+1

Which of the following pairs of functions is/are identical? (a) f(x)="tan"(tan^(-1)x)a n dg(x)="cot"(cot^(-1)x) (b) f(x)=sgn(x)a n dg(x)=sgn(sgn(x)) (c) f(x)=cot^2xdotcos^2xa n dg(x)=cot^2x-cos^2x (d) f(x)=e^(lnsec^(-1)x)a n dg(x)=sec^(-1)x

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

Find the intervals in which the functions are strictly increasing or decreasing: 6-9x-x^(2)

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