6. Which of the following best define(s) the triangle inequality?II. | a +b|<| a|+|6|I. | a + b|< | a | +|b|А. II onlyB. I and II onlyC. I onlyIII. | a + b|2|a |+|6|D. II and III onlyE. None of the above choices A, B,C or D7. Let A be a bounded subset of R and let sup A = 3. Which of the following is/arenot an attribute of 3?I. Ve > 0, 3 r E A Ə 3- e 0.A. {r €R :r > 3}B. {r €R :r < -1}C. {r €R :r < -1 and r> 3}.D. {r €R : -1 < x < 3}E. None of the above.9. Let a, b e R such that a < b. Which of these intervals is/are bounded?II. {r € R : r > a}I. (а, b)A. I and II onlyВ. II onlyC. I and III onlyIII. (-0,b)D. II and III onlyE. None of the above choices A, B,C or D

The tringle inequality is: a+b≤a+b

6. Which of the following best define(s) the triangle inequality? 1. | a + b|< |a|+ 16| II. | a +b|<|a|+16| III. | a +b|2|a |+16| A. II only B. I and II only C. I only D. II and III only E. None of the above choices A, B,C or D

6. Which of the following best define(s) the triangle inequality? 1. | a + b|< |a|+ 16| II. | a +b|<|a|+16| III. | a +b|2|a |+16| A. II only B. I and II only C. I only D. II and III only E. None of the above choices A, B,C or D

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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Question

6. Which of the following best define(s) the triangle inequality?
II. | a +b|<| a|+|6|
I. | a + b|< | a | +|b|
А. II only
B. I and II only
C. I only
III. | a + b|2|a |+|6|
D. II and III only
E. None of the above choices A, B,C or D
7. Let A be a bounded subset of R and let sup A = 3. Which of the following is/are
not an attribute of 3?
I. Ve > 0, 3 r E A Ə 3- e<r < 8
II. B<r V rE A.
III. If a E A, 3 r<aV r€ A then 3 <a.
A. I and II only
B. II and III only
С. I, I and III
D. II only
E. None of the above choices A, B,C or D
8. Let R be the set of all real numbers. Find the value(s) of r E R for
which a? – 2x – 3 > 0.
A. {r €R :r > 3}
B. {r €R :r < -1}
C. {r €R :r < -1 and r> 3}.
D. {r €R : -1 < x < 3}
E. None of the above.
9. Let a, b e R such that a < b. Which of these intervals is/are bounded?
II. {r € R : r > a}
I. (а, b)
A. I and II only
В. II only
C. I and III only
III. (-0,b)
D. II and III only
E. None of the above choices A, B,C or D

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