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(B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a > b> 0, then b-1 > a-1.

(B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a > b> 0, then b-1 > a-1.

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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please show the proof of (f), (h), (i)
Theorem Let a, b, c ER. (a) If a < b and b< c, then a < c. (Tra (b) If a < b, then a +c <b+c. (Addition F (c) If a < b and 0 < c, then ac < bc. (Multiplication (d) If a < b and c < 0, then bc < ac. (Multiplication (e) If a 0, then a2 = a· a > 0. (TB1>0 (g) If a > b and c> d, then a + c > b + d. Th) If a > b > 0 and c> d> 0, then ac > bd. i) If a> b> 0, then b-1> a-1.
Transcribed Image Text:Theorem Let a, b, c ER. (a) If a < b and b< c, then a < c. (Tra (b) If a < b, then a +c <b+c. (Addition F (c) If a < b and 0 < c, then ac < bc. (Multiplication (d) If a < b and c < 0, then bc < ac. (Multiplication (e) If a 0, then a2 = a· a > 0. (TB1>0 (g) If a > b and c> d, then a + c > b + d. Th) If a > b > 0 and c> d> 0, then ac > bd. i) If a> b> 0, then b-1> a-1.
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