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

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)

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

If f(x) = 2 sinx, g(x) = cos^(2) x , then the value of (f+g)((pi)/(3))

If f(x) = 2 sinx, g(x) = cos^(2) x , then the value of (f+g)((pi)/(3))

If f(x)=cos ec(x-(pi)/(3))cos ec(x-(pi)/(6)) then the value of int_(0)^((pi)/(2))f(x)dx is

Consider the function f(x)=(1-sinx)/((pi-2x)^(2)) where xne(pi)/(2)andf((pi)/(2))=lambda What is the value of lambda . If the function is continuous at x=(pi)/(2) ?

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