" 23."f(x)=sin x+cos x" in "[0,(pi)/(2)]

Verify Rolle's theorem for each of the following functions on indicated intervals; f(x)=sin^(2)x on 0<=x<=pi f(x)=sin x+cos x-1 on [0,(pi)/(2)]f(x)=sin x-sin2x on [0,pi]

Verify Rolle's theorem for each of the following functions: (i) f(x) = sin 2x " in " [0, (pi)/(2)] (ii) f(x) = (sin x + cos x) " in " [0, (pi)/(2)] (iii) f(x) = cos 2 (x - (pi)/(4)) " in " [0, (pi)/(2)] (iv) f(x) = (sin x - sin 2x) " in " [0, pi]

Find the maximum and minimum value of f(x)=sin x+(1)/(2)cos2x in [0,(pi)/(2)]

Statement 1: Let f(x)=sin(cos x) in [0,(pi)/(2)]* Then f(x) is decreasing in [0,(pi)/(2)] Statement 2:cos x is a decreasing function AA x in[0,(pi)/(2)]

If f_(1)(x)=2x, f_(2)x(=3 sin x-x cos x, for x in (0, (pi)/(2))

If f(x)=cos x+sin x, find f((pi)/(2))

Let f(x)=sin^(4)x-cos^(4)x int_(0)^((pi)/(2))f(x)dx =

If f_(1)(x)=2x,f_(2)(x)=3sin x-x cos x then for x in(0,(pi)/(2))

Let f(x)=1+x.sin x*[cos x]*0

f(x)=sqrt(3)cos x + sin x, x in [0, (pi)/(2)] is maximum for x = …………