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The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
F(X,Y) = 0. and take P to be the origin (0,0). Erasing terms of higher order than 1 would produce a 'linearised' equation reading L(X,Y) = 0. in which all terms X a Y b have been discarded if a + b > 1. We have two cases: L may be 0, or it may be the equation of a line.
Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...
This formula defines a closed curve contained in the rectangle −a ≤ x ≤ +a and −b ≤ y ≤ +b.The parameters and are the semi-diameters or semi-axes of the curve. The overall shape of the curve is determined by the value of the exponent , as shown in the following table:
The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d. ... They cannot be 1, because the logarithm function is ...
The first significant progress after Catalan made his conjecture came in 1850 when Victor-Amédée Lebesgue dealt with the case b = 2. [3] In 1976, Robert Tijdeman applied Baker's method in transcendence theory to establish a bound on a,b and used existing results bounding x,y in terms of a, b to give an effective upper bound for x,y,a,b.
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