#1 part I 2:31AA A learn-us-east-1-prod-fleet01-xythos.CSection 3.2 Homework (from the 5" Edition)1. Let x, y, and z be real numbers. Prove the following:[a] -(-x)= x[b] (-x)y = -(xy) and (- x)- y)= xy[c] If x = 0, then - 0 and[d] If xz = yz and z # 0 then x = y[e] If x 0, then x² > 0[S] 0 <1[g] !f x > 1, then x² > x[h] If 0 < x < 1 then x² <1[i] If x > 0, then > 0. If x < 0, then +< 0[j] !f 0 < x < y, then 0 < + 0 and y > 0 or[k] If xy > 0, then(ii) x< 0 and v<0[1] VNEN if 00 , thenx = 03. Prove: (x|)(y) = |xy| for all real numbers x and y.Vx, yER4. Prove: -| s |x – y|5. Prove: 4- y| < c, then |x| < |r| +cVx, yER6. Prove: " |x – y| < ɛ, Vɛ > 0, then x = yVx, yER7. Prove: 4 x, ,X3,...x, ER, then |x, + x, +.. + x,|sx, |+ |x,| + ... + |x_|

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Description: #1 part I 2:31AA A learn-us-east-1-prod-fleet01-xythos.CSection 3.2 Homework (from the 5" Edition)1. Let x, y, and z be real numbers. Prove the following:[a] -(-x)= x[b] (-x)y = -(xy) and (- x)- y)= xy[c] If x = 0, then - 0 and[d] If xz = yz and z #

1.(i) we have x,y and z ∈R and R is a feild with respect to addition and multiplication…

Answered: 2:31 AA A…

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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#1 part I

2:31
AA A learn-us-east-1-prod-fleet01-xythos.C
Section 3.2 Homework (from the 5" Edition)
1. Let x, y, and z be real numbers. Prove the following:
[a] -(-x)= x
[b] (-x)y = -(xy) and (- x)- y)= xy
[c] If x = 0, then - 0 and
[d] If xz = yz and z # 0 then x = y
[e] If x 0, then x² > 0
[S] 0 <1
[g] !f x > 1, then x² > x
[h] If 0 < x < 1 then x² <1
[i] If x > 0, then > 0. If x < 0, then +< 0
[j] !f 0 < x < y, then 0 < +<!
(i) x > 0 and y > 0 or
[k] If xy > 0, then
(ii) x< 0 and v<0
[1] VNEN if 0<x< y, then x" < y"
[m] If 0 < x < y, then 0 < /x < Jy
2. Prove: If x 2 0 and×sɛ for allɛ >0 , thenx = 0
3. Prove: (x|)(y) = |xy| for all real numbers x and y.
Vx, yER
4. Prove: -| s |x – y|
5. Prove: 4- y| < c, then |x| < |r| +c
Vx, yER
6. Prove: " |x – y| < ɛ, Vɛ > 0, then x = y
Vx, yER
7. Prove: 4 x, ,X3,...x, ER, then |x, + x, +.. + x,|sx, |+ |x,| + ... + |x_|

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$1 . (i) w e h a v e x, y a n d z \in R a n d R i s a f e i l d w i t h r e s p e c t t o a d d i t i o n a n d m u l t i p l i c a t i o n T h e r e i s o n e p r o p e r t i e s i n f e i l d (m u l t i p l i c a t i v e i n v e r s e) i f a \in R t h e r e e x i s t s a b \in R s u c h t h a t a . b = 1 l e t a = x \Rightarrow b = \frac{1}{x} a . b = 1 > 0 \Rightarrow a > 0, b > 0 o r a < 0, b < 0$

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