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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.
The first particular case of first order differential equations which we will seem is the linear first order differential equation. In this section, unlike many of the first order
use the bionomial theorem to expand x+2/(2-X)(WHOLE SQUARE 2)
If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y. (Ans:5, -2 (Not unique) Ans: Using Euclid's algorithm, the HCF (30, 72) 72 = 30 × 2 + 12
Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi
Ask queFind the normalized differential equation which has {x, xex} as its fundamental setstion #Minimum 100 words accepted#
how to find the sum of the measure of the interior angles of each convex polygon
ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB. Ans: Consider Δ ADE and Δ ABF ∠D = ∠B
Determine or find out if the subsequent series is convergent or divergent. If it converges find out its value. Solution To find out if the series is convergent we fir
Product and Quotient Rule : Firstly let's see why we have to be careful with products & quotients. Assume that we have the two functions f ( x ) = x 3 and g ( x ) = x 6 .
introduction
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