Let  f(x,y)=(cosx+ysinx)2. Let the maximum value of f(x,y) over all values of x for a given fixed value of y is called g(y). Let the smallest positive value x which achieves this maximum value of f(x,y) for a given y be h(y). If ∫2+√31h(y)g(y)dy=π2K, then value of K is equal to

Which of the following functions has a maximum y value of 4?y = cos x + 4y = cos( x + 4)y = 4cos xy = cos4 x

The region bounded by the x-axis and the part of the graph of y = cos x between x = −π/2 and x = π/2 is separated into two regions by the line x = k. If the area of the region for -π/2 ≤ x ≤ k is three times the area of the region for k ≤ x , then k =

The largest interval (a, b) of k ∈ R,for which the point (0, 0) is the critical point of the function f(x, y) = x2 + kxy + y

Nonlinear ProgrammingThe largest interval (a, b) of k ∈ R,for which the point (0, 0) is the critical point of the function f(x, y) = x2 + kxy + yans.[0, 1](−∞, ∞)[-1,-1][1,0]This Question Is

The sum of squares of all possible values of k, for which area of the region bounded by the parabolas 2y2=kx and ky2=2(y−x) is maximum, is equal to :