Problem 1. The absolute value of a real number x, denoted by [x], is defined { Let x, y ER and a ≥ 0. Prove the following statements. (a) x≤ a if and only if -a ≤ x ≤a. (b) |xy| = |x|y|- (c) |x+y| ≤ |x| + |y|. as |x| = = x if x ≥ 0 -x if x < 0.
Problem 1. The absolute value of a real number x, denoted by [x], is defined { Let x, y ER and a ≥ 0. Prove the following statements. (a) x≤ a if and only if -a ≤ x ≤a. (b) |xy| = |x|y|- (c) |x+y| ≤ |x| + |y|. as |x| = = x if x ≥ 0 -x if x < 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Problem 1. The absolute value of a real number x, denoted by [x], is defined
{
Let x, y ER and a > 0. Prove the following statements.
(a) x≤ a if and only if -a ≤ x ≤a.
(b) |xy| = |x|y|-
(c) |x+y| ≤ |x| + |y|.
as
|x| =
=
x if x ≥ 0
-x if x < 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F690bc708-737a-4036-8bde-cd8ee17ec8dd%2F238f5b17-7ce1-4668-8073-7ef123c5f290%2F3y2ucbt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1. The absolute value of a real number x, denoted by [x], is defined
{
Let x, y ER and a > 0. Prove the following statements.
(a) x≤ a if and only if -a ≤ x ≤a.
(b) |xy| = |x|y|-
(c) |x+y| ≤ |x| + |y|.
as
|x| =
=
x if x ≥ 0
-x if x < 0.
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