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indeterminate expression

Indeterminate Expression

An undefined expression which can have a value if arrived at as a limit.

Note: Another way to think about indeterminate expressions is to see them as a disagreement between two rules for simplifying an expression. For example, one way to think about is this: The 0 in the numerator makes the fraction "equal" 0, but the 0 in the denominator makes the fraction "equal" ±∞. This conflict makes the expression indeterminate.

 

Common indeterminate expressions:

                00        1        ∞0        ∞ – ∞

Example:

The limit

seems to evaluate to , which is indeterminate. In fact,

since sin x and x are approximately equal to each other for values of x near 0.

Note that this limit can also be computed using l’Hôpital’s rule.

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