Question

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.

The volume of a sphere is increasing at the rate of 8 cm³/sec. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

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

Find the area of the parallelogram whose diagonals are represented by the vectors $\stackrel{\rightarrow}{a}\$ = $2{\hat{i}}-3{\hat{j}}+4{\hat{k}}$ and ${\vec{b}}=2{\hat{i}}-{\hat{j}}+2{\hat{k}}$

If P(F) = 0·35 and P(E U F) = 0·85 and E and F are independent events. Find P(E).

Show that the function f(x) = x³ – 3x² + 6x – 100 is increasing on R.

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