If \lim_{x\rightarrow a^+}f(x) \neq \lim_{x\rightarrow a^-}f(x) then either f(a) = \lim_{x\rightarrow a^+}f(x) or f(a) = \lim_{x\rightarrow a^-}f(x) .

If \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x) then \lim_{x\rightarrow a}f(x) = f(a).

If \lim_{x\rightarrow a}f(x) exists and is a real number then \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x).

If \lim_{x\rightarrow a}f(x) exists then \lim_{x\rightarrow a}f(x) = f(a). 

If \lim_{x\rightarrow a}f(x) exists and is a real number then \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x) provided the domain of the function includes values slightly greater than and slightly less than a.

If \lim_{x\rightarrow a^+}f(x) \neq \lim_{x\rightarrow a^-}f(x) then f(a) is undefined.

\lim_{x\rightarrow a}f(x) = f(a) provided the function f is defined when x=a.

If \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x) then \lim_{x\rightarrow a}f(x) exists and is equal to the limit found by the one sided limits.