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Each limit is taken as n→ ∞. (1) x →>> 1 for all x > 0. (2) "0 if |x| < 1. (3) →0 for all a > 0. (11.4.1) (4) → 0 for all real x. n! In n (5) → 0. n (6) n¹/n → 1. X n (7) + ← ex for all real x. (1) PROOF Fix any x > 0. Since If x 0, then →>> as 118.

Each limit is taken as n→ ∞. (1) x →>> 1 for all x > 0. (2) "0 if |x| < 1. (3) →0 for all a > 0. (11.4.1) (4) → 0 for all real x. n! In n (5) → 0. n (6) n¹/n → 1. X n (7) + ← ex for all real x. (1) PROOF Fix any x > 0. Since If x 0, then →>> as 118.

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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Explain why these limits hold in 11.4.1

Each limit is taken as n→ ∞. (1) x →>> 1 for all x > 0. (2) "0 if |x| < 1. (3) →0 for all a > 0. (11.4.1) (4) → 0 for all real x. n! In n (5) → 0. n (6) n¹/n → 1. X n (7) + ← ex for all real x. (1) PROOF Fix any x > 0. Since If x 0, then →>> as 118.
Transcribed Image Text:Each limit is taken as n→ ∞. (1) x →>> 1 for all x > 0. (2) "0 if |x| < 1. (3) →0 for all a > 0. (11.4.1) (4) → 0 for all real x. n! In n (5) → 0. n (6) n¹/n → 1. X n (7) + ← ex for all real x. (1) PROOF Fix any x > 0. Since If x 0, then →>> as 118.
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