(追記) (追記ここまで)
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.