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(c) Recall e = 2.71828... is Euler's constant and e² is the exponential function. Since e > 2, you may assume that lim ()² = = ∞o. Show that lim I→∞ I Hint: you may use the result of part (b) and a new Squeeze Theorem in one of the lectures.

(c) Recall e = 2.71828... is Euler's constant and e² is the exponential function. Since e > 2, you may assume that lim ()² = = ∞o. Show that lim I→∞ I Hint: you may use the result of part (b) and a new Squeeze Theorem in one of the lectures.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 47E
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question c only please

x z→∞ ln x (a) For all positive integers n ≥ 1, prove that 2" > 2n. 2. Here you will prove that lim ∞ without any use of L'Hopital's Rule. (b) For all real numbers x ≥ 1, prove that 2. Hint:Define n = = [x].
Transcribed Image Text:x z→∞ ln x (a) For all positive integers n ≥ 1, prove that 2" > 2n. 2. Here you will prove that lim ∞ without any use of L'Hopital's Rule. (b) For all real numbers x ≥ 1, prove that 2. Hint:Define n = = [x].
(c) Recall e = 2.71828... is Euler's constant and e is the exponential function. Since e> 2, you may assume that lim 2² (²)² = x+x = ∞o. Show that lim I→∞ I Hint: you may use the result of part (b) and a new Squeeze Theorem in one of the lectures.
Transcribed Image Text:(c) Recall e = 2.71828... is Euler's constant and e is the exponential function. Since e> 2, you may assume that lim 2² (²)² = x+x = ∞o. Show that lim I→∞ I Hint: you may use the result of part (b) and a new Squeeze Theorem in one of the lectures.
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