Question

Which condition defines continuity of a real-valued function \[f\] at \[x=c\]?

Options

• \[f(c)\] is not defined

• \[\lim_{x\to c}f(x)\ne f(c)\]

• \[\lim_{x\to c}f(x)=f(c)\]

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

Answer 1

A function is continuous at \[x=c\] exactly when its limit as \[x\] approaches \[c\] equals its value at \[c\]. Thus, \[\lim_{x\to c}f(x)=f(c)\] is required.