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| < ε whenever x ∈ D and |x-c| < δ.
(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 (sn) in D that converges to c with Sn ≠ c for ail n, the sequence (f(sn)) converges to L.
(d) If f does not have a limit at c, then there exists a sequence (sn) in D with each sn ≠ c such that (sn) converges to c, but (f(sn)) is divergent.
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