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{ if a >0 if a <0 a 3. (a) The absolute value of a eR is defined as Ja = V6 > 0 and -a Ja| = b , if and only if a = ±b. Find all values x ER of that satisfy the equation |2.x2 – 1| = |r+ 2|. (b) Show that ER, x2- 4x +5 > 0. %3D %3D 2² +1 (c) Prove that if A = :x ER then A is a bounded subset of R. x2 - 2x +3

{ if a >0 if a <0 a 3. (a) The absolute value of a eR is defined as Ja = V6 > 0 and -a Ja| = b , if and only if a = ±b. Find all values x ER of that satisfy the equation |2.x2 – 1| = |r+ 2|. (b) Show that ER, x2- 4x +5 > 0. %3D %3D 2² +1 (c) Prove that if A = :x ER then A is a bounded subset of R. x2 - 2x +3

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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if a >0 if a <0 3. (a) The absolute value of a e R is defined as |a >0 and +b. Find all values r E R of that satisfy the equation Jal = b , if and only if a = |2x2 – 1| = |x + 2|. (b) Show that x ER, x2 - 4x + 5 > 0. x2 +1 (c) Prove that if A :x €R then A is a bounded subset of R. x2 – 2x + 3
Transcribed Image Text:if a >0 if a <0 3. (a) The absolute value of a e R is defined as |a >0 and +b. Find all values r E R of that satisfy the equation Jal = b , if and only if a = |2x2 – 1| = |x + 2|. (b) Show that x ER, x2 - 4x + 5 > 0. x2 +1 (c) Prove that if A :x €R then A is a bounded subset of R. x2 – 2x + 3
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