The function `f(x)=(ln(pi+x))/(ln(e+x))` is increasing in `(0,oo)` decreasing in `(0,oo)` increasing in `(0,pi/e),` decreasing in `(pi/e ,oo)` decreasing in `(0,pi/e),` increasing in `(pi/e ,oo)`

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is a. increasing in (0,3a) decreasing in (3a, 4a) b. increasing in (a, 4a) decreasing in (5a ,oo) c. increasing in (0,4a) d. none of these

Prove that the function given by f(x) = cos x is (a) decreasing in (0, pi ) (b) increasing in (pi, 2pi) , and (c) neither increasing nor decreasing in (0, 2pi) .

Show that the function given by f (x) = sin x is (a) increasing in (0,(pi)/(2)) (b) decreasing in ((pi)/(2) ,pi) (c) neither increasing nor decreasing in (0, pi )

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Statement 2: If both f(x)a n dg(x) are increasing in (a , b),t h e nf(x)g(x) must be increasing in (a,b).

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

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

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

Prove that the function f given by f (x) = log |cos x| is decreasing on (0,(pi)/(2)) and increasing on ((3pi)/(2) ,2pi) .