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Let e be a positive real number. Prove or disprove that n E N(n²+e).

Let e be a positive real number. Prove or disprove that n E N(n²+e).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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3. Asymptotic notation. For each part of this question, you may (but are not required to) use any of the following facts. • Fact 1: Vn E Z, n < 2" • Fact 2: Vx, y E R†, x < y A log2(x) < log2(y) • Fact 3: Vx, y E R, x < y A 2° < 2º You may NOT use any of the facts from pages 92-95 in the Course Notes. Your proofs must depend only on elementary properties of logarithms and exponential functions, together with the facts above. (Ь) Let e be a positive real number. Prove or disprove that n E N(n'+E).
Transcribed Image Text:3. Asymptotic notation. For each part of this question, you may (but are not required to) use any of the following facts. • Fact 1: Vn E Z, n < 2" • Fact 2: Vx, y E R†, x < y A log2(x) < log2(y) • Fact 3: Vx, y E R, x < y A 2° < 2º You may NOT use any of the facts from pages 92-95 in the Course Notes. Your proofs must depend only on elementary properties of logarithms and exponential functions, together with the facts above. (Ь) Let e be a positive real number. Prove or disprove that n E N(n'+E).
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