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3. If x >0 show that |(₁ + 2) ¹/³² - ( ₁ + 1 ² - √ ² ) | ≤ 3 ²². )1/3 S Use this inequality to approximate 1.2 and 2.

3. If x >0 show that |(₁ + 2) ¹/³² - ( ₁ + 1 ² - √ ² ) | ≤ 3 ²². )1/3 S Use this inequality to approximate 1.2 and 2.

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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3. If r>0 show that 1 |(1 + 2)¹/³ − ( 1 + 3 2 − 3 2²)| ≤ 512. s Use this inequality to approximate 1.2 and 2.
Transcribed Image Text:3. If r>0 show that 1 |(1 + 2)¹/³ − ( 1 + 3 2 − 3 2²)| ≤ 512. s Use this inequality to approximate 1.2 and 2.
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Step 1: Binomial theorem for fractional index

We recall the binomial theorem for fractional index. 

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