Question

Which one-sided-limit condition is required for continuity at \[x=c\]?

Options

• \[\lim_{x\to c^-}f(x)\ne\lim_{x\to c^+}f(x)=f(c)\]

• \[\lim_{x\to c^-}f(x)\] and \[\lim_{x\to c^+}f(x)\] need not exist

• \[\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)\ne f(c)\]

• \[\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=f(c)\]

Answer 1

For continuity, both the left-hand limit and right-hand limit must exist. They must be equal to each other and to \[f(c)\].