Remember:
Proof by mathematical induction requires the fulfilment of both the conditions (i) and (ii) as stated above. Condition (i) creates the basis for carrying out induction and condition (ii) gives us the right to make a general assertion or of an automatic extensi..
De Moivre's Theorem
De Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometr..
De Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometr..Study the following examples
1. The numbers 2, 3, 5 and 8. 2. The solutions of the equation x 2 - 2x - 15 = 0. 3. The letters of the word "Chase". 4. People living in our locality. 5. The students Mary, Hillary, Catherine. 6. The workers who are absent from the factory. 7. The capital cities of Asia. 8. The positive even int..
Introduction
.02 cm. The unit of accuracy required is hundredth of a centimeter. Therefore, only digit 2 is significant. The 0 after decimal indicates the magnitude of measurement. Therefore, the 0 after decimal point is not significant. .02 cm has one significant figure. To sum up the above examples: (a) For a..
Summary
A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is..
A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is..Examples of recurring decimal:
(a) (b) Hence we state the classical definition of rational numbers: Find a rational number between two rational numbers To obtain the required number, add numerators and denominators as shown below: ..
(a) (b) Hence we state the classical definition of rational numbers: Find a rational number between two rational numbers To obtain the required number, add numerators and denominators as shown below: ..Sets Summary
Summary - A well-defined collection of definite objects is called a set. In roster method of representing a set, all the elements are listed in the set. In property method of representing a set, all the elements are represented by stating all the properties which are satisfied by the elem..
Transition State Theory
Transition State Theory - According to this theory, the reactant molecules must come together to form an arrangement of atoms/molecules that facilitates the formation of products. This arrangement of the reacting species is called the transitio..
Transition State Theory - According to this theory, the reactant molecules must come together to form an arrangement of atoms/molecules that facilitates the formation of products. This arrangement of the reacting species is called the transitio..
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