Question

Which condition makes a function discontinuous at \[x=a\]?

Options

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

• \[\lim_{x\to a}f(x)=f(a)\]

• \[\lim_{x\to a}f(x)\ne f(a)\]

• \[f(a)\] is defined and both limits are equal to \[f(a)\].

Answer 1

A function is discontinuous when it fails the continuity condition. In particular, it is discontinuous if \[\lim_{x\to a}f(x)\ne f(a)\].