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In [[mathematics]], a number of the expressions that may be encountered in [[calculus]] are considered to be '''indeterminate forms''', and must be treated as symbolic only, until more careful discussion has taken place. The most common one is
:<math>0/0</math>
which has no definite meaning, considering that [[division by zero]] is not a meaningful operation in [[arithmetic]]. Further examples are
:<math>\infty/\infty</math>
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:<math>\infty^0</math>
:<math>\infty-\infty,</math>
all of which are
If ''f''(''x'') and ''g''(''x'') both approach 0 as ''x'' approaches some number, or ''x'' approaches ∞ or −∞, then :<math>{f(x) \over g(x)}</math>
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If one uses the evaluation of the limit above for the purpose of ''proving'' that (''d''/''dx'') ''x''<sup>''n''</sup> = ''nx''<sup>''n''−1</sup> and one uses L'Hopital's rule and the fact that (''d''/''dx'') ''x''<sup>''n''</sup> = ''nx''<sup>''n''−1</sup> in the evaluation of the limit, then one's reasoning is circular and therefore fallacious.
[[Category:Mathematical analysis]]
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