Live practice

For f(x)=|x|/x when x≠0 and f(0)=0, determine lim(x→0)f(x).

Find the origin-centred-vertex parabola with focus (−2,0).

The perpendicular from the origin to a line ends at (−2,9). Find that line.

For distinct complex numbers α and β with |β|=1, evaluate |(β−α)/(1−conjugate(α)β)|.

Complete every requested part of exercise 3.2, question 18: cos 3x = 4 cos3 x – 3 cos x We have, cos 3x = cos (2x +x) = cos 2x cos x – sin 2x sin x = (2cos2 x – 1) cos x – 2sin x cos x sin x = (2cos2 x – 1) cos x – 2cos x (1 – cos2 x) = 2cos3 x – cos x – 2cos x + 2 cos3 x = 4cos3 x – 3cos x. 3 tan x – tan 3 x π

Let \(f(x)=x^2\) for \(0\le x\le3\) and \(f(x)=3x\) for \(3\le x\le10\). Let \(g(x)=x^2\) for \(0\le x\le2\) and \(g(x)=3x\) for \(2\le x\le10\). Show that \(f\) is a function but \(g\) is not.

Why is Wurtz reaction not preferred for the preparation of alkanes containing odd number of carbon atoms? Illustrate your answer by taking one example.

Explain why sodium extract is acidified with nitric acid before the silver nitrate test for halogens.

In Ostwald’s process for the manufacture of nitric acid, the first step involves the oxidation of ammonia gas by oxygen gas to give nitric oxide gas and steam. What is the maximum weight of nitric oxide that can be obtained starting only with \(10.00\,\mathrm{g}\). of ammonia and \(20.00\,\mathrm{g}\) of oxygen ?

Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume? (a) PCl5 (g) PCl3 (g) + Cl2 (g) (b) CaO (s) + CO2 (g) CaCO3 (s) (c) 3Fe (s) + 4H2O (g) Fe3O4 (s) + 4H2 (g)