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Prove that if a(x) = |r|, the absolute value function, then a E C(R). (Use 1.9.)

Prove that if a(x) = |r|, the absolute value function, then a E C(R). (Use 1.9.)

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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2.20 † Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use Exercise 1.9.) For reference: 1.9 † Prove: For all a and b in R, |la| – l6|| < la – bl. Intuitively, this says that la| and |b| cannot be farther apart than a and b are. (Hint: Write |a| = |(a – b) + b| and use the triangle inequality. Then do the same thing for |6|.)
Transcribed Image Text:2.20 † Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use Exercise 1.9.) For reference: 1.9 † Prove: For all a and b in R, |la| – l6|| < la – bl. Intuitively, this says that la| and |b| cannot be farther apart than a and b are. (Hint: Write |a| = |(a – b) + b| and use the triangle inequality. Then do the same thing for |6|.)
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