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)={(1-sin^3x)/(3cos^2x) if x pi/2 find a and b. .

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

If f'(x) = tan^(-1)(Sec x + tan x), x in (-pi/2 , pi/2) and f(0) = 0 then the value of f(1) is

The minimum value of f(x)= "sin"x, [(-pi)/(2),(pi)/(2)] is

Let f(x)={:{((kcosx)/(pi-2x)',xne(pi)/(2)),(3",",x=(pi)/(2).):} If lim_(xto(pi)/(2))f(x)=f((pi)/(2)), find the value of k.

Let f(x) = x cos^(-1)(-sin|x|) , x in (-pi/2,pi/2)

If F(x) = {(sin{cosx})/(x-pi/2),x!=pi/2 and 1,x=pi/2, where {.} represents the fractional part function, then lim_(xto pi//2)f(x) is

Let f(x) = tan x, x in (-pi/2,pi/2)and g(x) = sqrt(1-x^2) then g(f(x)) is

Let f(x)=|(cos x,e^(x^2) , 2x cos^2x/2),(x^2, sec x, sinx+x^3),(1,2,x+tan x)| then the value of int_(-pi/2)^(pi/2)(x^2+1)(f(x)+f''(x))dx

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to