(1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute value (x + yl of their sum is the sum [x] + [y] of their absolute values. Corel
(1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute value (x + yl of their sum is the sum [x] + [y] of their absolute values. Corel
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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Question
(NQ1)
TYPE ONLY THE ANSWERS AND FORMULAS, DO NOT HANDWRITTEN IT. SHOW THE STEP BY STEP SOLUTION.
NOTE:
For no.1:
Recall that |x| = x iff x >= 0
Show ab < 0 leads to a contradiction.
Then assume ab>=0.
Prove by cases:
(i) Let ab=0.
(ii) Let ab > 0
ANSWER NUMBER 1 ONLY!
![(1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute
of their sum is the sum |x|+|y| of their absolute values.
Oue|x + yl
(2) Let x, y and z be real numbers. Show that the distance between a real number x and z is the sum of the distances
between x and y and between y and z if and only if y = [x, z]. Illustrate geometrically on the real line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1ca438c-94de-43e9-82e6-54ad1f024274%2F87eb2ecd-f675-4864-921c-1fc05a30cb1c%2Ffxg4f4b_processed.png&w=3840&q=75)
Transcribed Image Text:(1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute
of their sum is the sum |x|+|y| of their absolute values.
Oue|x + yl
(2) Let x, y and z be real numbers. Show that the distance between a real number x and z is the sum of the distances
between x and y and between y and z if and only if y = [x, z]. Illustrate geometrically on the real line.
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