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The derivative of the function at a point is the slope of the line tangent to the curve at the point. Slope of the constant function is zero, because the tangent line to the constant function is horizontal and its angle is zero. In other words, the value of the constant function, y, will not change as the value of x increases or decreases.
Newton–Cotes formula for. In numerical analysis, the Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for numerical integration (also called quadrature) based on evaluating the integrand at equally spaced points. They are named after Isaac Newton and Roger Cotes.
Gauss–Legendre quadrature. In numerical analysis, Gauss–Legendre quadrature is a form of Gaussian quadrature for approximating the definite integral of a function. For integrating over the interval [−1, 1], the rule takes the form: where. xi are the roots of the n th Legendre polynomial. This choice of quadrature weights wi and quadrature ...
Romberg's method. In numerical analysis, Romberg's method[1] is used to estimate the definite integral by applying Richardson extrapolation [2] repeatedly on the trapezium rule or the rectangle rule (midpoint rule). The estimates generate a triangular array. Romberg's method is a Newton–Cotes formula – it evaluates the integrand at equally ...
In mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive real roots is at most the number of sign changes in the sequence of polynomial's coefficients (omitting zero coefficients), and the difference ...
Table of contents. A table of contents from a book about cats with descriptive text. A table of contents, usually headed simply Contents and abbreviated informally as TOC, is a list, usually found on a page before the start of a written work, of its chapter or section titles or brief descriptions with their commencing page numbers.
Rule of division (combinatorics) In combinatorics, the rule of division is a counting principle. It states that there are n/d ways to do a task if it can be done using a procedure that can be carried out in n ways, and for each way w, exactly d of the n ways correspond to the way w. In a nutshell, the division rule is a common way to ignore ...
Rule of product. The elements of the set {A, B} can combine with the elements of the set {1, 2, 3} in six different ways. In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the intuitive idea that if there are a ways of doing ...