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Hint. You want to show |a| – |6| < |a – b| and -(lal – |b|) < la – bl.

Hint. You want to show |a| – |6| < |a – b| and -(lal – |b|) < la – bl.

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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Real math analysis 

Please help me solve problem 7.2.3

 

4:47 M A personal.psu.edu/ecb5/ASO Problem 7.2.3. (a) Prove Lemma 7.2.2. Lemma 7.2.2. Triangle Inequality: Let a and b be real numbers. Then la + 비 < lal + |0. Reverse Triangle Inequality: Let a and b be real numbers. Then lal-1이 < la-비 in-context Hint. For the Reverse Triangle Inequality, consider |a| = |a – b + b|. (b) Show ||a| – |b|| < |a – bl. Hint. You want to show lal-1이 < la-b이 and -(lal-1) < la-이. II
Transcribed Image Text:4:47 M A personal.psu.edu/ecb5/ASO Problem 7.2.3. (a) Prove Lemma 7.2.2. Lemma 7.2.2. Triangle Inequality: Let a and b be real numbers. Then la + 비 < lal + |0. Reverse Triangle Inequality: Let a and b be real numbers. Then lal-1이 < la-비 in-context Hint. For the Reverse Triangle Inequality, consider |a| = |a – b + b|. (b) Show ||a| – |b|| < |a – bl. Hint. You want to show lal-1이 < la-b이 and -(lal-1) < la-이. II
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