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Grapher is a computer program bundled (with no additional cost) with macOS since version 10.4 that is able to create 2D and 3D graphs from simple and complex equations. It includes a variety of samples ranging from differential equations to 3D-rendered Toroids and Lorenz attractors. It is also capable of dealing with functions and compositions ...
In addition to graphing both equations and inequalities, it also features lists, plots, regressions, interactive variables, graph restriction, simultaneous graphing, piecewise function graphing, recursive function graphing, polar function graphing, two types of graphing grids – among other computational features commonly found in a ...
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...
Equation. The first use of an equals sign, equivalent to 14 x + 15 = 71 in modern notation. From The Whetstone of Witte by Robert Recorde of Wales (1557). [1] In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.
In mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve . The graphical representation of the graph of a function is also known as a plot . In the case of functions of two variables – that is ...
Implicit curve as level curves of the surface. In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation . In general, every implicit curve is defined by an equation of the form.
1) Compare this with the parabola x 2 = 4 f y , {\displaystyle x^{2}=4fy,} (2) which has its vertex at the origin, opens upward, and has focal length f (see preceding sections of this article). Equations (1) and (2) are equivalent if R = 2 f . Therefore, this is the condition for the circle and parabola to coincide at and extremely close to the origin. The radius of curvature at the origin ...
The equation defining a plane curve expressed in polar coordinates is known as a polar equation. In many cases, such an equation can simply be specified by defining r as a function of φ. The resulting curve then consists of points of the form (r(φ), φ) and can be regarded as the graph of the polar function r.
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