Prove the following inequalities: 1. x x2 - ² ≤ ln (1 + x) ≤ x for x > 0 2 2. sin xx - Xx x³ for x > 0 6

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section: Chapter Questions
Problem 23CLR
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Prove the following inequalities:
1. x
x2
- ² ≤ ln (1 + x) ≤ x for x > 0
2
2. sin xx
-
Xx
x³ for x > 0
6
Transcribed Image Text:Prove the following inequalities: 1. x x2 - ² ≤ ln (1 + x) ≤ x for x > 0 2 2. sin xx - Xx x³ for x > 0 6
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