Consider a function, `f(x)=2/3ln^(3/2) (sinx+cosx)` for `x in (0,pi/2)` The value of `Lim_(x->pi/2) f(x)/(pi/2-x)^(3/2)`

Consider a function,f(x)=(2)/(3)ln(sin x+cos x)^((3)/(2)) for x in(0,(pi)/(2)) The value of lim_(x rarr(pi)/(2))(f(x))/((pi)/(2)-x) is

Let f (x) = sin x - cos x. Then the value of lim _( x to pi/2) ""(f (x)- f ((pi)/(2)))/(x - (pi)/(2)) is

Let f(x) =(kcosx)/(pi-2x) if x!=pi/2 and f(x)=3 if x=pi/2 then find the value of k if lim_(x->pi/2) f(x)=f(pi/2)

Let f(x)=sinx+2cos^2x , x in [pi/6,(2pi)/3] , then maximum value of f(x) is

Let f(x)=|x|+|sinx|, x in (-pi/ 2,3pi/2). Then , f is

The function f(x)=(sinx)^(tan^(2)x) is not defined at x=(pi)/(2) . The value of f((pi)/(2)) such that f is continuous at x=(pi)/(2) is

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

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)