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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.
In mathematics, a limit is the value that a function ... (see Indeterminate form), yet as x moves arbitrarily close to 1, f(x) correspondingly approaches 2: [13] f(0.9)
The limit of f of x, as x approaches p, exists, and it equals L and write, [6] ... This rule uses derivatives to find limits of indeterminate forms 0/0 or ±∞/ ...
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:
The expression 0 0 is an indeterminate form: Given real-valued functions f(t) and g(t) approaching 0 (as t approaches a real number or ±∞) with f(t) > 0, the limit of f(t) g(t) can be any non-negative real number or +∞, or it can diverge, depending on f and g.
When given a ratio between two functions, the limit of this ratio can be evaluated by computing the limit of each function separately. Where the limit of the function in the denominator is infinity, and the numerator does not allow the ratio to be well determined, the limit of the ratio is said to be of indeterminate form. [9]
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.
Indeterminate forms – algebraic expressions gained in the context of limits. The indeterminate forms include 0 0, 0/0, 1 ...