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In mathematics, a quadratic function of a single variable is a function of the form [1] = + +,,where is its variable, and , , and are coefficients.The expression + + , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.
A different technique, which goes back to Laplace (1812), [3] is the following. Let = =. Since the limits on s as y → ±∞ depend on the sign of x, it simplifies the calculation to use the fact that e −x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity.
The Taylor series of any polynomial is the polynomial itself.. The Maclaurin series of 1 / 1 − x is the geometric series + + + +. So, by substituting x for 1 − x, the Taylor series of 1 / x at a = 1 is
The golden ratio was called the extreme and mean ratio by Euclid, [2] and the divine proportion by Luca Pacioli; [3] it also goes by other names. [b]Mathematicians have studied the golden ratio's properties since antiquity.
Pell's equation for n = 2 and six of its integer solutions. Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form =, where n is a given positive nonsquare integer, and integer solutions are sought for x and y.
Why is x²+xy+y² called a binomial based on having two variables and not a trinomial based on have three terms (in two variables). If you look at the article Trinomial the third example given is 3ts+9t+5s -- which has two variables and is not called a binomial. 192.96.44.56 13:39, 13 March 2024 (UTC)
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Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.