Question

When is \[f(x)\] non-removable discontinuous at \[x=a\]?

Options

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

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

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

• \[f(a)=\lim_{x\to a}f(x)\]

Answer 1

A non-removable discontinuity occurs when the one-sided limits are different. Since LHL is not equal to RHL, \[\lim_{x\to a}f(x)\] does not exist.