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Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.
This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions
An example of a limit where is not defined at is given below. Consider the function =. then f(1) is not defined (see Indeterminate form), yet as x moves arbitrarily close to 1, f(x) correspondingly approaches 2: [13]
Subsequential limit – the limit of some subsequence; Limit of a function (see List of limits for a list of limits of common functions) One-sided limit – either of the two limits of functions of real variables x, as x approaches a point from above or below; Squeeze theorem – confirms the limit of a function via comparison with two other ...
Indeterminate form; Interchange of limiting operations; Iterated limit; L. L'Hôpital's rule; ... Limit of a function; Limit of a sequence; List of limits; M. Moore ...
Other indeterminate forms, such as 1 ∞, 0 0, ∞ 0, 0 · ∞, and ∞ − ∞, can sometimes be evaluated using L'Hôpital's rule. We again indicate applications of L'Hopital's rule by = . For example, to evaluate a limit involving ∞ − ∞, convert the difference of two functions to a quotient:
See Indeterminate form. --Kinu t / c 19:34, 15 May 2016 (UTC) Indeterminate forms are quite common with +-infinity. With only real numbers (i.e. no infinities) there are only 4 indeterminate forms; 0/0, 0 to the 0, the zeroth root of 1, and the logarithm of 1 in base 1. Georgia guy 20:41, 15 May 2016 (UTC)
L'Hôpital's rule uses derivatives to find limits of indeterminate forms 0/0 or ±∞/∞, and only applies to such cases. Lamarck's theory of evolution has two laws: The first can be paraphrased as "use it or lose it". The second is the more famous law of soft inheritance.