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Example:
E, F, G, H, ..
Change of subject of formula
In the formula I is called the subject of the formula. To make 'P' the subject of the formula: P x T x R = 100 x ..
Increasing and Decreasing Functions
This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. Let f be a function defined on an interval I and let x 1 and x 2 be any two points on I. (i) f is said to be increasing in the interval ..
Maxima and Minima
A function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of 'a', such that f(a) f(x) for all x I The number f(a) is called the local maximum of f(x). The point a is called the point of maximu..
Increasing and Decreasing Functions
Increasing and Decreasing Functions - This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. Let f be a function defined on an interval I and let x 1 and x 2 be any two points on I. (i) f is sai..
Theorem:
The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B = C Hence the in..
Repeaters
In long-distance lines, losses are so high that satisfactory operation becomes impossible without the use of amplification. Amplifiers for telephone service are known as repeaters, and they must of course function in both directions along the line. Repeater stations are ordinarily install..
Method II
a cos q + b sin q = c -----(i) (i) can be written as or a (1- t 2 ) + 2bt - c (1+t 2 ) = 0 This is a quadratic in 't' and can be solved...
Maxima and Minima
A function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of 'a', such that f(a) f(x) for all x I The number f(a) is called the local maximum of f(x). The point a is called the point of maximum. Note that when 'a' is the point of local maxima, f(x) is increasing for a..
One mole is the number of atoms in a 12g sample of carbon-12
The number N A , given by N A = 6.023x10 2 3 mol - 1 is called Avogadro's number, named after Italian scientist Amadeo Avogadro (1776-1856), who suggested that all gases contain the same number of atoms or molecules when they occupy the same volume under the same conditions of temperature and ..
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