Let f : D → R and let c be an accumulation point of D. Mark each statement True or False. Justify each answer. (a) limx → c f (x) = L iff for every ε > 0 there exists a δ > 0 such that | f (x) – L | ∈...

Let f : D → R and let c be an accumulation point of D. Mark each statement True or False. Justify each answer.

(a) limx → c f (x) = L iff for every ε > 0 there exists a δ > 0 such that | f (x) – L | <>∈ D and | x – c | <>

(b) limx → c f (x) = L iff for every deleted neighborhood U of c there exists a neighborhood V of L such that f (U ∩ D) ⊆ V.

(c) limx → c f (x) = L iff for every sequence (s_n) in D that converges to c with s_n
≠ c for all n, the sequence ( f (s_n)) converges to L.

(d) If f does not have a limit at c, then there exists a sequence (s_n) in D with each s_n
≠ c such that (s_n) converges to c, but ( f (s_n)) is divergent.