Given `A = {x: pi/6 le x le pi/3}` and f (x) = cos x -x(1 + x), find f (A).

If f(x) = |sin x - cosx| , find f' ( pi//6)

If f(x) = |sinx| + | cos x| , find f'((3pi)/(4))

At x = 5pi/6 , f(x) = 2 sin 3x + 3 cos 3 x is

If 0 le x le 3 pi , 0 le y le 3 pi and cos x * sin y=1 , then find the possible number of values of the orederd pair (x,y) .

If 0 le x le pi and cosx=-4/5 then cos(x/2) is equal to:

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b .

{:(f(x) = cos x and H_(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)/(2) = (pi)/(2)-x,(pi)/(2) lt x le pi),(f(x) = cos x and H_(2) (x) = max {f(t), o le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x","(pi)/(2) lt x le pi),(g(x) = sin x and H_(3)(x) = min{g(t),0 le t le x},),(0 le x le (pi)/(2)=(pi)/(2) - x, (pi)/(2) le x le pi),(g(x) = sin x and H_(4)(x) = max{g(t),0 le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x, (pi)/(2) lt x le pi):} Which of the following is true for H_(1) (x) ?

Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x le 0),(x-1",",1 lt x le 2):} and g(x)=f(|x|) +|f(x)| . Then find g(x) .

The values of a and b so that the function f(x) = {{:(x + a sqrt(2) sin x",",0 le x lt pi//4),(2 x cot x + b",",pi//4 le x le pi//2),(a cos 2 x - b sin x",",pi//2 lt x le pi):} is continuous for x in [0, pi] , are

If f'(x) = a sin x + b cos x and f'(0) = 4,f(0) = 3, f((pi)/(2))= 5 , find f(x).