<Dd> lim x → c f (x) g (x). (\ displaystyle \ lim _ (x \ to c) f (x) ^ (g (x)).) </Dd> <P> If the functions f and g are analytic at c, and f is positive for x sufficiently close (but not equal) to c, then the limit of f (x) will be 1 . Otherwise, use the transformation in the table below to evaluate the limit . </P> <P> The expression 1 / 0 is not commonly regarded as an indeterminate form because there is not an infinite range of values that f / g could approach . Specifically, if f approaches 1 and g approaches 0, then f and g may be chosen so that (1) f / g approaches + ∞, (2) f / g approaches − ∞, or (3) the limit fails to exist . In each case the absolute value f / g approaches + ∞, and so the quotient f / g must diverge, in the sense of the extended real numbers . (In the framework of the projectively extended real line, the limit is the unsigned infinity ∞ in all three cases .) Similarly, any expression of the form a / 0, with a ≠ 0 (including a = + ∞ and a = − ∞), is not an indeterminate form since a quotient giving rise to such an expression will always diverge . </P> <P> The expression 0 is not an indeterminate form . The expression 0 has the limiting value 0 for the given individual limits, and the expression 0 is equivalent to 1 / 0 . </P>

Limit of one to the power of infinity