information:extraction, structural:expansion
Indeterminate form 0

The following limits illustrate that the expression 0 0 {\displaystyle 0^{0}} is an indeterminate form:

Thus, in general, knowing that lim x → c f (x) = 0 {\displaystyle \textstyle \lim _{x\to c}f(x)\;=\;0} and lim x → c g (x) = 0 {\displaystyle \textstyle \lim _{x\to c}g(x)\;=\;0} is not sufficient to evaluate the limit

If the functions f {\displaystyle f} and g {\displaystyle g} are analytic at c {\displaystyle c}, and f {\displaystyle f} is positive for x {\displaystyle x} sufficiently close (but not equal) to c {\displaystyle c}, then the limit of f (x) g (x) {\displaystyle f(x)^{g(x)}} will be 1 {\displaystyle 1}. Otherwise, use the transformation in the table below to evaluate the limit.