1. Use the ę notation to prove the following limits: lim n→∞ [n^2+ 3ncos(2n+1)+2] / [n^2−nsin(4n+3)+4]...

1. Use the ę notation to prove the following limits:

lim n→∞ [n^2+ 3ncos(2n+1)+2] / [n^2−nsin(4n+3)+4] = 1

2. Let {an} a sequence converging to L > 0. Show ∃N ∈ N, ∀n ∈ N, n ≥ N, an > 0

3.Let {an} a sequence converging to L. Let {bn} a sequence such that ∃Nb ∈ N, ∀n ∈ N, n ≥ Nb, an = bn. Show that {bn} converges to L as well.

Thank you. Please complete proofs fully.

Expert Solution

Colby Messinger answered 6 months ago

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