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2. a. Prove using the formal definition of a limit that the following sequence converges: -n3 + 2n – 211 2n3 + 1+4 =1

2. a. Prove using the formal definition of a limit that the following sequence converges: -n3 + 2n – 211 2n3 + 1+4 =1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Proofs must be clear, coherent, concise, and complete, and examples should be verified to satisfy required properties. 1. a. Show that for all sets A, B, and C, if A CBUC, then A nc+ø or A C B. b. Disprove: For all sets A, B, C, and D, (AUC) x (BUD) C (A x B) u(C x D). 2. a. Prove using the formal definition of a limit that the following sequence converges: +oo -n3 + 2n - 21 213 + и + 4 1=1 b. Let {a,} be a sequence of real numbers. We say that {a;} decreases without bound, written lim an = -00, iff 11=1 (VM < 0)(3N > 0) (n € N)(n > N = an < M). Show that lim (-n*) = -0o.
Transcribed Image Text:Proofs must be clear, coherent, concise, and complete, and examples should be verified to satisfy required properties. 1. a. Show that for all sets A, B, and C, if A CBUC, then A nc+ø or A C B. b. Disprove: For all sets A, B, C, and D, (AUC) x (BUD) C (A x B) u(C x D). 2. a. Prove using the formal definition of a limit that the following sequence converges: +oo -n3 + 2n - 21 213 + и + 4 1=1 b. Let {a,} be a sequence of real numbers. We say that {a;} decreases without bound, written lim an = -00, iff 11=1 (VM < 0)(3N > 0) (n € N)(n > N = an < M). Show that lim (-n*) = -0o.
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