Solve: `|-2x^2+1+e^x+sinx|=|2x^2-1|+e^x+|sinx|,x in [0,2pi]dot`

If f(x)=2sinx-x^(2) , then in x in [0, pi]

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

Find the number of solution(s) of the following questions (a) x^2 + x + 1 + sinx = 0, x in [0, 2pi] (b) x^2 + x + 1 + sinx = 0, x in [pi, 2pi] (c) x^2 + x + sinx = 0, x in [0, pi]

Solve |sin 3x + sinx | + |sin 3x - sinx |= sqrt3, - (pi)/(2) lt x lt (pi)/(2).

lim_(x to 0) (e^x-e^sinx)/(x-sinx)

lim_(x rarr 0)(e^x-e^sinx)/(2(x-sinx))=

Solve the equation , 5sinx+5/(2sinx)-5=2sin^2x+1/2sin^2x if x in (0,pi).