Find the x coordinates of all the points on the curve `y =sin 2x-2sin x,0lex<2pi`, where `(dy)/(dx)=0`.

Find the x-coordinates of all the points on the curve y=sin 2x - 2sin x , 0 le x < 2 pi

Find the co-ordinates of the points on the curve 4y=x^2 , which are nearest to the point (0, 5)

Find the coordinates of the point on the curve y=x^2 – 3x + 2 where the tangent is perpendicular to the straight line y = x

Find the area of the region bounded by the curve y = sin x between x = 0 and x= 2pi .

Find the area of the region bounded by the curve y=sin x , x=-pi/2,x=pi/2 .

Answer the following questions:Find the coordinates of a point on x+y+3=0 ,whose distance from x+2y+2=0 is sqrt5

If tangents are drawn to the circle x^2 +y^2=12 at the points where it intersects the circle x^2+y^2-5x+3y-2=0 , then the coordinates of the point of intersection of those tangents are

A particle moves along the curve 6y= x^3 + 2. Find the points on the curve at which y-coordinate is changing 8 times as fast as the X-coordinate.

Find the derivative of the inverse functionof the followings, and also find their value at the points indicated against them: y = sin (x-2) + x^2 , at x = 2