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Although the set of integers caters to a larger audience, it is inadequate. This inadequacy has led to the formulation of Rational numbers. Rational numbers are of the form p/q, where p and q are integers and q ≠ 0. The numbers like 2/3,-5/4 are examples of rational numbers. The set of rational numbers are denoted by Q and generally expressed as:
In the set of rational numbers if you consider any of the element say -2/5, we observe that the quotient is - 0.4. Similarly if you consider 7/8, the quotient is 0.875. In both these cases the decimal part is terminating. By terminating, we understand that the division process is coming to an end. Now, in the same set, consider the element 6/7. For this number the quotient is 0.857142857142...... In this case we observe that the decimal part is (i) not terminating and (ii) repeating.
But on occasions we find decimals which neither terminate nor repeat. For instance, consider a number like 65/67. The quotient is of the form 0.970149253..... In this quotient we neither find the decimal terminating nor repeating. Numbers whose decimals are non-terminating and non-repeating are included in a set of numbers called irrational numbers.
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2x^3+5x^2+2x+5
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Consider the equation x 2 y′′+ xy′- y = 4x ln x (a) Verify that x is a solution to the homogeneous equation. (b) Use the method of reduction of order to derive the second
The Mean Value Theorem : In this section we will discuss the Mean Value Theorem. Before we going through the Mean Value Theorem we have to cover the following theorem. Ro
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If the expression 9y - 5 represents a certain number, which of the following could NOT be the translation? a. five less than nine times y b. five less than the sum of 9 and y c
Example : Determine the equation of the line which passes through the point (8, 2) and is, parallel to the line given by 10 y+ 3x = -2 Solution In both of parts we are goi
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