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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.
Similarly, the limit of f as x approaches minus infinity is L, ... Other indeterminate forms may be manipulated into this form. Given two functions f(x) ...
Infinity plus negative infinity is an indeterminate form (a variant of infinity minus infinity that is one of Trovatore's above list of indeterminate forms.) Georgia guy 17:38, 16 May 2016 (UTC) More generally, there are many, many kinds of infinity. I don't mean many sizes, I mean many kinds.
However, when a function is constructed by dividing two functions whose separate limits are both equal to , then the limit of the result cannot be determined from the separate limits, so is said to take an indeterminate form, informally written . (Another indeterminate form, , results from dividing two functions whose limits both tend to ...
The hyperbola = /.As approaches ∞, approaches 0.. In mathematics, division by infinity is division where the divisor (denominator) is ∞.In ordinary arithmetic, this does not have a well-defined meaning, since ∞ is a mathematical concept that does not correspond to a specific number, and moreover, there is no nonzero real number that, when added to itself an infinite number of times ...
In the second case, indeterminate generally indicates that a value or property can have many meaningful definitions. Additionally, it seems to be generally accepted that undefined values may not be safely used within a particular formal system, whereas indeterminate values might be, depending on the relevant rules of the particular formal ...
In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets.
It can be indeterminate in a weak sense, like 1/0 (but perhaps a bit stronger). For example, as x approaches 0 from the right, (1/x) 1/x approaches infinity (from the left), while (1/x)-1/x approaches zero (from the right). But nothing of this form can converge to any non-zero finite value (because the logarithm must converge to infinity).