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f(x) = maximum (sin t, 0 le t le x), 0 ...

f(x) = maximum `(sin t, 0 le t le x), 0 le x le 2pi` discuss the continuity of this function at `x=pi/2` f(x) = maximum `(sin t,0 le t le x), 0 le x le 2pi`

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{:(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_(2) (x) ?

{:(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_(3) (x) ?

{:(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_(4)(x) ?