Question

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

Options

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

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

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

• \[\lim_{x\to a}f(x)\] does not exist because \[f(a)=0\].

Answer 1

For a removable discontinuity, the left-hand and right-hand limits are equal, so the limit exists. However, that common limit is not equal to \[f(a)\].