Indeterminate form: Difference between revisions

Revision as of 13:55, 30 September 2022

Revision as of 13:57, 30 September 2022

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An expression that arises by ways other than applying the algebraic limit theorem may have the same form of an indeterminate form. However it is not appropriate to call an expression "indeterminate form" if the expression is made outside the context of determining limits.

For example, <math>0/0</math> which arises from substituting <math>0~</math> for <math>x</math> in the equation <math>f(x)=|x|/(|x-1|-1)</math> is not an indeterminate form since this expression is not made in the determination of a limit (it is in fact undefined as [[division by zero]]).

Another example is the expression <math>0^0</math>. Whether this expression is left undefined, or is defined to equal <math>1</math>, depends on the field of application and may vary between authors. For more, see the article [[Zero to the power of zero]]. Note that <math>0^\infty </math> and other expressions involving infinity [[#Expressions that are not indeterminate forms|are not indeterminate forms]].

== Some examples and non-examples ==