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An example of an equation involving x and y as unknowns and the parameter R is x 2 + y 2 = R 2 . {\displaystyle x^{2}+y^{2}=R^{2}.} When R is chosen to have the value of 2 ( R = 2), this equation would be recognized in Cartesian coordinates as the equation for the circle of radius of 2 around the origin.
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset. Step function: A finite linear combination of indicator functions of half-open intervals. Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function. Sawtooth wave; Square wave ...
A function :, with domain X and codomain Y, is bijective, if for every y in Y, there is one and only one element x in X such that y = f(x). In this case, the inverse function of f is the function f − 1 : Y → X {\displaystyle f^{-1}:Y\to X} that maps y ∈ Y {\displaystyle y\in Y} to the element x ∈ X {\displaystyle x\in X} such that y = f ...
In mathematics, a linear equation is an equation that may be put in the form + … + + =, where , …, are the variables (or unknowns), and ,, …, are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions , provided they do not contain any of the variables.
"x^y = y^x - commuting powers". Arithmetical and Analytical Puzzles. Torsten Sillke. Archived from the original on 2015-12-28. dborkovitz (2012-01-29). "Parametric Graph of x^y=y^x". GeoGebra. OEIS sequence A073084 (Decimal expansion of −x, where x is the negative solution to the equation 2^x = x^2)
Burgers' equation; Darcy–Weisbach equation; Dirac equation. Dirac equation in the algebra of physical space; Dirac–Kähler equation; Doppler equations; Drake equation (aka Green Bank equation) Einstein's field equations; Euler equations (fluid dynamics) Euler's equations (rigid body dynamics) Relativistic Euler equations; Euler–Lagrange ...
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
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