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[c] If x 0, then -0 and

[c] If x 0, then -0 and

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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_|
Transcribed Image Text: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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