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Calculate the following limits of functions using the sequential character- ization from Theorem 4.2.3 (and theorems about limits of sequences, if required). (a) lim +1. x 4 2+31 (b) lim ²-1. 2-1 x-1 (c) lim 4x³ 3x² + 7x - 11. x-0 -

Calculate the following limits of functions using the sequential character- ization from Theorem 4.2.3 (and theorems about limits of sequences, if required). (a) lim +1. x 4 2+31 (b) lim ²-1. 2-1 x-1 (c) lim 4x³ 3x² + 7x - 11. x-0 -

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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Theorem 4.2.3 (Sequential Criterion for Functional Limits). Given a function f A → R and a limit point c of A, the following two statements are equivalent: (i) lim f(x) = L. I-C (ii) For all sequences (rn) ≤ A satisfying 2n c and (n)→c, it follows that f(n) → L.
Transcribed Image Text:Theorem 4.2.3 (Sequential Criterion for Functional Limits). Given a function f A → R and a limit point c of A, the following two statements are equivalent: (i) lim f(x) = L. I-C (ii) For all sequences (rn) ≤ A satisfying 2n c and (n)→c, it follows that f(n) → L.
Calculate the following limits of functions using the sequential character- ization from Theorem 4.2.3 (and theorems about limits of sequences, if required). (a) lim +1. x 4 2+31 (b) lim ²-1 2-1 2-1' (c) lim 4x³ 3x² + 7x - 11. x-0
Transcribed Image Text:Calculate the following limits of functions using the sequential character- ization from Theorem 4.2.3 (and theorems about limits of sequences, if required). (a) lim +1. x 4 2+31 (b) lim ²-1 2-1 2-1' (c) lim 4x³ 3x² + 7x - 11. x-0
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