Mathematical concepts

Limiting case (mathematics)

In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values. For example: * In statistics, the limiting case of the binomial distribution is the Poisson distribution. As the number of events tends to infinity in the binomial distribution, the random variable changes from the binomial to the Poisson distribution. * A circle is a limiting case of various other figures, including the Cartesian oval, the ellipse, the superellipse, and the Cassini oval. Each type of figure is a circle for certain values of the defining parameters, and the generic figure appears more like a circle as the limiting values are approached. * Archimedes calculated an approximate value of π by treating the circle as the limiting case of a regular polygon with 3 × 2n sides, as n gets large. * In electricity and magnetism, the long wavelength limit is the limiting case when the wavelength is much larger than the system size. * In economics, two limiting cases of a demand curve or supply curve are those in which the elasticity is zero (the totally inelastic case) or infinity (the infinitely elastic case). * In finance, continuous compounding is the limiting case of compound interest in which the compounding period becomes infinitesimally small, achieved by taking the limit as the number of compounding periods per year goes to infinity. A limiting case is sometimes a degenerate case in which some qualitative properties differ from the corresponding properties of the generic case. For example: * A point is a degenerate circle, namely one with radius 0. * A parabola can degenerate into two distinct or coinciding parallel lines. * An ellipse can degenerate into a single point or a line segment. * A hyperbola can degenerate into two intersecting lines. * v * t * e (Wikipedia).

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2.2 The Limit of a Function

OpenStax Calculus Volume 1

From playlist Calculus 1

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Limit doesn't exist 2 variables example

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From playlist Engineering Mathematics

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3 The limit laws

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From playlist Life Science Math: Limits in calculus

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In this video I do an example of computing limits from a graph with infinities.

From playlist Limits

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More resources available at www.misterwootube.com

From playlist Modelling Financial Situations

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From playlist Summer of Math Exposition 2 videos

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This video covers the laws of limits and how we use them to evaluate a limit. These laws are especially handy for continuous functions. More theorems about limits are introduced in later videos. For more videos visit http://www.mysecretmathtutor.com

From playlist Calculus

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Limiting Sum (3 of 3: General Formula)

More resources available at www.misterwootube.com

From playlist Modelling Financial Situations

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Limit of a function

Free ebook http://tinyurl.com/EngMathYT A simple example of how to evaluate limits of a function. Such ideas are seen in high school and unversity calculus.

From playlist A first course in university mathematics

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From playlist Abel Lectures

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On the existence of thermodynamic potentials for quantum systems... by Takahiro Sagawa

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From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday

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From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

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Yang-Mills for mathematicians (Lecture - 01) by Sourav Chatterjee

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From playlist MIT Calculus Revisited: Single Variable Calculus

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Wolfram Physics Project: Working Session Tuesday, Nov. 2, 2021 [Topos Theory]

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Wolfram Physics Project: Working Session Tuesday, Nov. 16, 2021 [Metamathematics]

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From playlist Wolfram Physics Project Livestream Archive

Related pages

Mathematical object | Ellipse | Statistics | Archimedes | Special case | Superellipse | Cassini oval | Poisson distribution | Parabola | Point (geometry) | Line segment | Cartesian oval | Mathematics | Pi | Radius | Generic property | Hyperbola | Demand curve | Binomial distribution | Degeneracy (mathematics) | Regular polygon | Circle | Wavelength