A function `f(x)` is such that `f(x+pi/2)=pi/2-|x|AAxdotF in df(pi/2),ifi te xi s t sdot`

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

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 to - pi ) f(x)/(sin (sin x))=

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

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

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

If f(x)=sinx ,AAx in [0,pi/2],f(x)+f(pi-x)=2,AAx in (pi/2,pi)a n df(x)=f(2pi-x),AAx in (pi,2pi), then the area enclosed by y=f(x) and the x-axis is pis qdotu n i t s (b) 2pis qdotu n i t s 2s qdotu n i t s (d) 4s qdotu n i t s

A function f(x) is defined as follows: f(x)={{:(x+pi," for ",x""in[-pi","0)),(picosx," for ",x""in[0","(pi)/(2)]),((x-(pi)/(2))^(2)," for ",x""in((pi)/(2)","pi]):} Consider the following statements : 1. The function f(x) is continuos at x=0. 2. The function f(x) is continuous at x=(pi)/(2) . Which of the above statements is/are correct?

Let f:(0, pi)->R be a twice differentiable function such that (lim)_(t->x)(f(x)sint-f(x)sinx)/(t-x)=sin^2x for all x in (0, pi) . If f(pi/6)=-pi/(12) , then which of the following statement(s) is (are) TRUE? f(pi/4)=pi/(4sqrt(2)) (b) f(x)<(x^4)/6-x^2 for all x in (0, pi) (c) There exists alpha in (0, pi) such that f^(prime)(alpha)=0 (d) f"(pi/2)+f(pi/2)=0

A function y=f(x) satisfies f''(x)=-(1)/(x^(2))-pi^(2)sin(pi x)f'(2)=pi+(1)/(2) and f(1)=0 then value of f((1)/(2)) is