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Indeterminate form

In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form. 

Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

Cardinal number

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.

Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Divergent series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

Division by zero

In mathematics, division by zero is division where the divisor (denominator) is zero.

Extended real number line

In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).

François-Napoléon-Marie Moigno

Abbé François-Napoléon-Marie Moigno (15 April 1804 – 14 July 1884) was a French Catholic priest and one time Jesuit, as well as a physicist and author.

Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them.

L'Hôpital's rule

In mathematics, and more specifically in calculus, L'Hôpital's rule or L'Hospital's rule uses derivatives to help evaluate limits involving indeterminate forms.

Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.

Limit of a function

Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

Limit point

In mathematics, a limit point (or cluster point or accumulation point) of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.

Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

Projectively extended real line

In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the number line by a point denoted.

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

Undefined (mathematics)

In mathematics, undefined has several different meanings, depending on the context.

Zero to the power of zero

Zero to the power of zero, denoted by 00, is a mathematical expression with no obvious value.

References

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