A function `f(x)` is such that `f(x+pi/2)=pi/2-|x|AAx`. Find `f(pi/2)`, if it exists.

Let f(x) be a differentiable function such that f'(x)=sinx+sin4xcosx. Then f'(2x^(2)+(pi)/(2))"at "x=sqrt((pi)/(2)) is equal to

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

Examination the function f(x) given by f(x)={((cosx)/(pi/2-x) ,, x != pi/2),(1 ,, x = pi/2):} ; for continuity at x=pi/2

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/(2))=-(3pi^(2))/(4) , then lim_(xto -pi^+) (f(x))/(sin(sinx)) is equal to

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)=-(3pi^2)/4, then lim_(x->-pi)(f(x))/("sin"(sinx) is equal to (a) 0 (b) pi (c) 2pi (d) none of these

Consider a function f defined by f(x)=sin^(-1) sin ((x+sinx)/2) AA x in [0,pi] which satisfies f(x)+f(2pi-x)=pi AA x in [pi, 2pi] and f(x)=f( 4pi-x) for all x in [2pi,4pi] then If alpha is the length of the largest interval on which f(x) is increasing, then alpha =

Consider the function f(x)=(sin 2x)^(tan^(2)2x), x in (pi)/(4) . The value of f((pi)/(4)) such that f is continuous at x=(pi)/(4) is

Discuss the continuity of the function f(x) ={:{((1+cos x)/(tan^2 x) ", "x ne pi),((1)/(2) ", " x=pi):}, at x=pi .

A function y=f(x) satisfies A function y=f(x) satisfies f" (x)= -1/x^2 - pi^2 sin(pix) ; f'(2) = pi+1/2 and f(1)=0 . The value of f(1/2) then

If f(x) is continuous in [0,pi] such that f(pi)=3 and int_0^(pi/2)(f(2x)+f^(primeprime)(2x))sin2x dx=7 then find f(0).