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What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or p should be greater than q. We express the same as p = q or p > q or p ≥ q. If p is greater than q, then, is not p - q a positive number? It is. Statements like p < q or p > q are called inequalities. We employ the concept of inequalities to understand sets referred to as intervals. We define an interval as a range of values from which the real number "p" is likely to assume values. In this context, interval is more restricted as compared to a set of real numbers which ranges from + ∞ to - ∞ . We should note that ' ∞ ' is not a real number and it is employed only because of convenience.
Explain the Graphical Technique of Linear Equations by using this figure.
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What is Perfect Squares ? Any number that can be written as an integer to the power of two is called a perfect square. For example, 4 can be written as 2 2 4 is a "perfect sq
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Proof of: ∫ f(x) + g(x) dx = ∫ f(x) dx + ∫g(x) dx It is also a very easy proof. Assume that F(x) is an anti-derivative of f(x) and that G(x) is an anti-derivative of
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If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
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