Question: Let \(f: D \rightarrow \mathbb{R}\) and let \(c\) be an accumulation point of \(D\). Mark each statement True or False. Justify each answer.

1. \(\lim _{x \rightarrow c} f(x)=L\) iff for every \(\varepsilon>0\) there exists a \(\delta>0\) such that \(|f(x)-L|<\varepsilon\) whenever \(x \in D\) and \(|x-c|<\delta\).
2. \(\lim _{x \rightarrow c} f(x)=L\) iff for every deleted neighborhood \(U\) of \(c\) there exists a neighborhood \(V\) of \(L\) such that \(f(U \cap D) \subseteq V\)
3. \(\lim _{x \rightarrow c} f(x)=L\) iff for every sequence \(\left(s_{n}\right)\) in \(D\) that converges to \(c\) with \(s_{n} \neq c\) for all \(n\), the sequence \(\left(f\left(s_{n}\right)\right)\) converges to \(L\).
4. If \(f\) does not have a limit at \(c\), then there exists a sequence \(\left(s_{n}\right)\) in \(D\) with each \(s_{n} \neq c\) such that \(\left(s_{n}\right)\) converges to \(c\), but \(\left(f\left(s_{n}\right)\right)\) is divergent.

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