Indeterminate form

In calculus, the expressions

are indeterminate forms; if f(x) and g(x) both approach 0 as x approaches some number, or x approaches ∞ or −∞, then

can approach any real number or ∞ or −∞, or fail to converge to any point on the extended real number line, depending on which functions f and g are; similar remarks are true of the other indeterminate forms displayed above. For example,

and

Direct substitution of the number that x approaches into either of these functions leads to the indeterminate form 0/0, but both limitss actually exist and are 1 and 14 respectively.

The indeterminate form does not imply the limit does not exist. In many cases, algebraic elimination, L'Hôpital's rule, or other methods can be used to simplify the expression so the limit can be more easily evaluated.