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Applications of "squeeze lemma" (i) Prove that if p > 0 then limn→∞ NP (ii) Let z € C, and suppose that |z| < 1. Prove that limn→∞ z = 0. = 0 and limn→∞ p¹/n = 1.

Applications of "squeeze lemma" (i) Prove that if p > 0 then limn→∞ NP (ii) Let z € C, and suppose that |z| < 1. Prove that limn→∞ z = 0. = 0 and limn→∞ p¹/n = 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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**Applications of the "Squeeze Lemma"** (i) Prove that if \( p > 0 \) then \( \lim_{n \to \infty} \frac{1}{n^p} = 0 \) and \( \lim_{n \to \infty} p^{1/n} = 1 \). (ii) Let \( z \in \mathbb{C} \), and suppose that \( |z| < 1 \). Prove that \( \lim_{n \to \infty} z^n = 0 \).
Transcribed Image Text:**Applications of the "Squeeze Lemma"** (i) Prove that if \( p > 0 \) then \( \lim_{n \to \infty} \frac{1}{n^p} = 0 \) and \( \lim_{n \to \infty} p^{1/n} = 1 \). (ii) Let \( z \in \mathbb{C} \), and suppose that \( |z| < 1 \). Prove that \( \lim_{n \to \infty} z^n = 0 \).
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