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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.
Indeterminate (variable), a symbol that is treated as a variable; Indeterminate system, a system of simultaneous equations that has more than one solution; Indeterminate equation, an equation that has more than one solution; Indeterminate form, an algebraic expression with certain limiting behaviour in mathematical analysis
A fundamental property of an indeterminate is that it can be substituted with any mathematical expressions to which the same operations apply as the operations applied to the indeterminate. Some authors of abstract algebra textbooks define an indeterminate over a ring R as an element of a larger ring that is transcendental over R.
Here is a basic example involving the exponential function, which involves the indeterminate form 0 / 0 at x = 0: + = (+) = + = This is a more elaborate example involving 0 / 0 . Applying L'Hôpital's rule a single time still results in an indeterminate form.
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)
In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. [1] For example, the equation a x + b y = c {\displaystyle ax+by=c} is a simple indeterminate equation, as is x 2 = 1 {\displaystyle x^{2}=1} .
A (real) polynomial is an expression of the form a 0 x 0 + ⋅⋅⋅ + a n x n, where x is an indeterminate, and the coefficients a i are real numbers. Polynomials are added termwise, and multiplied by applying the distributive law and the usual rules for exponents. With these operations, polynomials form a ring R[x].
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)