Evaluate dx as limit of sums.

It is given that for the function f(x) = x³ - 6x² + ax + b Rolle’s theorem holds in [1, 3] with c = . Find the values of ‘a’ and ‘b’.

Determine for what values of x, the function is strictly increasing o strictly decreasing

OR

Find the point on the curve y =x³ – 11x + 5 at which the tangent is y = x – 11.

Find the area of the region bounded by the y-axis, y = cos x and y = sin x, .

Can y = ax + be a solution of the following differential equation?

If no, find the solution of the D.E. (*).

OR

Check whether the following differential equation is homogeneous or not

Find the general solution of the differential equation using substitution y=vx.