Provide an Appropriate Response $\rightarrow$ A from the Left Exists, the Limit of F(x) As to Conclude

Provide an appropriate response.
-What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a?

A) The limit of f(x) as x $\rightarrow$ a from the left exists, the limit of f(x) as $\rightarrow$ a from the right exists, and at least one of these limits is the same as f(a) .
B) The limit of f(x) as $\rightarrow$ a from the left exists, the limit of f(x) as $\rightarrow$ a from the right exists, and these two limits are the same.
C) Either the limit of f(x) as $\rightarrow$ a from the left exists or the limit of f(x) as $\rightarrow$ a from the right exists
D) f(a) exists, the limit of f(x) as $\rightarrow$ a from the left exists, and the limit of f(x) as $\rightarrow$ a from the right exists.