Question

The total revenue received from the sale of x units of a product is given by R(x) = 3x² + 36x + 5 in rupees. Find the marginal revenue when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.

Find : $\textstyle\int$$\frac{d x}{\sqrt{3-2\,x-x^{2}}}$

Find : $\textstyle\int$$\sqrt{2x-x^{2}\ d x}$

Find the general solution of the differential equation ${\frac{d y}{d x}}+{\frac{2}{x}}y=x$

The radius r of a right circular cylinder is increasing at the rate of 5 cm/min and its height h, is decreasing at the rate of 4 cm/min. When r= 8 cm and h = 6 cm, find the rate of change of the volume of cylinder.

Find the sum of the order and the degree of the following differential equations : ${\frac{d^{2}y}{d x^{2}}}+{3{\sqrt\frac{{d y}}{d x}}}+(1+x)=0$

From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.