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)

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

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) = 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

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

If f(x)=int(sinx)/(cos^(2)x)(1-3sin^(3)x)dx , then value of (f(0)-f(pi)+(9pi)/2) is