1. (a) Let an→ 2. Prove from first principles (i.e. give a direct e-N proof) that a → 4. (b) Let an → 4. Prove that (an) has a subsequence which converges either to 2 or -2. (c) Let a →→ 4. Prove from first principles (i.e. give a direct e-N proof) that |an| → 2.
1. (a) Let an→ 2. Prove from first principles (i.e. give a direct e-N proof) that a → 4. (b) Let an → 4. Prove that (an) has a subsequence which converges either to 2 or -2. (c) Let a →→ 4. Prove from first principles (i.e. give a direct e-N proof) that |an| → 2.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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![1. (a) Let an 2. Prove from first principles (i.e. give a direct e-N proof) that az → 4.
(b) Let a → 4. Prove that (an) has a subsequence which converges either to 2 or
-2.
(c) Let a →→ 4. Prove from first principles (i.e. give a direct ɛ-N proof) that
2.
an](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2F4caf4cb1-501b-4980-8661-2a76dcf1a093%2Fybpe7ka_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (a) Let an 2. Prove from first principles (i.e. give a direct e-N proof) that az → 4.
(b) Let a → 4. Prove that (an) has a subsequence which converges either to 2 or
-2.
(c) Let a →→ 4. Prove from first principles (i.e. give a direct ɛ-N proof) that
2.
an
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