Show that the function f given by `f(x)=tan^(-1)(sinx+cosx),` `x" ">" "0` is always an strictly increasing function in `(0,pi/4)` .

Show that the function given by f(x)=e^(2x) is strictly increasing on R.

Show that the function f(x) given by f(x)={(sinx)/x+cosx ,x!=0 and 2,x=0 is continuous at x=0.

Prove that f(x)=tan ^(-1)(sin x + cos x ),x gt 0 f(0,pi/4) is increasing function

Show that the function f given by f(x)=x^3-3x^2+4x ,x in R is strictly increasing on R.

Show that the function given by f(x) = 7x-3 is strictly increasing on R.

Show that f(x)=tan^(-1)(sinx+cosx) is an increasing function on the interval (0,\ pi//4) .

Prove that the function f given by f (x) = log cos x is strictly decreasing on (0,pi/2) and strictly increasing on (pi/2,pi) prove that the function f given by f(x) = log sin x is strictly decreasing on ( 0 , pi/2) and strictly increasing on ( pi/2 , pi) ..

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)

Prove that the function f given by f(x)=logcosx is strictly increasing on (-pi//2,\ 0) and strictly decreasing on (0,\ pi//2) .

Find the intervals in which the function f given by f(x)=sinx-cosx,0lexle2π is strictly increasing or strictly decreasing.