Question

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

if $|\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}|$ =60, $|\stackrel{\rightarrow}{a}-\stackrel{\rightarrow}{b}|$=40 and $\stackrel{\rightarrow}{a}\$=22,then find $\stackrel{\rightarrow}{b}\$.

If P(E) = 7/13, P(F) = 9/3 and P(E' / F') = 4/3, then evaluate : (i) P(E / F) (ii) P(E / F)

Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).

The radius r of a right circular cylinder is decreasing at the rate of 3 cm/min. and its height h is increasing at the rate of 2 cm/min. When r =7 cm and h = 2 cm, find the rate of change of the volume of cylinder. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$

Find the integrating factor of the differential equation ${\frac{d y}{d x}}+y\ =\ {\frac{1+y}{x}}$

A particle moves along the curve 6y = x³ + 2. Find the points on the curve at which y-coordinate is changing 2 times as fast as x-coordinate.