Active Calculus 2nd Ed

At which values of \(a\) does \(\lim_{x \to a} f(x)\) not exist?

At which values of \(a\) is \(f(a)\) not defined?

At which values of \(a\) does \(f\) have a limit, but \(\lim_{x \to a} f(x) \ne f(a)\text{?}\)

State all values of \(a\) for which \(f\) is not continuous at \(x = a\text{.}\)

Which condition is stronger, and hence implies the other: \(f\) has a limit at \(x = a\) or \(f\) is continuous at \(x = a\text{?}\) Explain, and hence complete the following sentence: “If \(f\) at \(x = a\text{,}\) then \(f\) at \(x = a\text{,}\)” where you complete the blanks with has a limit and is continuous, using each phrase once.