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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
L'Hôpital's rule (/ ˌ l oʊ p iː ˈ t ɑː l /, loh-pee-TAHL) or L'Hospital's rule, also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives. Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be easily ...
According to Hankel (1871), the modern concept of limit originates from Proposition X.1 of Euclid's Elements, which forms the basis of the Method of exhaustion found in Euclid and Archimedes: "Two unequal magnitudes being set out, if from the greater there is subtracted a magnitude greater than its half, and from that which is left a magnitude ...
This rule uses derivatives to find limits of indeterminate forms 0/0 or ±∞/∞, and only applies to such cases. Other indeterminate forms may be manipulated into this form. Given two functions f(x) and g(x), defined over an open interval I containing the desired limit point c, then if:
The indeterminate form is because the division function is discontinuous at (0,0). Note that the indeterminate form is "0/0", not 'f(0)', which is not an indeterminate form. Also, the sentence you are editing is describing a binary operation, not a unary function as your example above provides. — Carl (CBM · talk) 20:49, 11 June 2007 (UTC)
[22] Knuth (1992) contends more strongly that 0 0 "has to be 1"; he draws a distinction between the value 0 0, which should equal 1, and the limiting form 0 0 (an abbreviation for a limit of f(t) g(t) where f(t), g(t) → 0), which is an indeterminate form: "Both Cauchy and Libri were right, but Libri and his defenders did not understand why ...
A limit of a sequence of points () in a topological space is a special case of a limit of a function: the domain is in the space {+}, with the induced topology of the affinely extended real number system, the range is , and the function argument tends to +, which in this space is a limit point of .