The triangle inequality: | a + b | ≤ | a | + | b | for any real numbers a and b. [Hint: For a real number x , what is x 2 ? ]

Question

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Answer 1

Question

Chapter 8.2, Problem 27E

(a)

To determine

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

(b)

To determine

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

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Answer 2

Question

Chapter 8.2, Problem 27E

(a)

To determine

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

(b)

To determine

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Expert Solution & Answer

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Answer 3

Question

Chapter 8.2, Problem 27E

(a)

To determine

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

(b)

To determine

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Expert Solution & Answer

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Answer 4

Question

Chapter 8.2, Problem 27E

(a)

To determine

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

(b)

To determine

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Expert Solution & Answer

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See solution

Answer 5

Chapter 8.2, Problem 27E

(a)

To determine

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

(b)

To determine

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Answer 6

Chapter 8.2, Problem 27E

(a)

To determine

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

Answer 7

Chapter 8.2, Problem 27E

(a)

To determine

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

Answer 8

(b)

To determine

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Answer 9

(b)

To determine

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 8.1 - Prob. 1TFQ Ch. 8.1 - Prob. 2TFQ Ch. 8.1 - Prob. 3TFQ Ch. 8.1 - Prob. 4TFQ Ch. 8.1 - Prob. 5TFQ Ch. 8.1 - Prob. 6TFQ Ch. 8.1 - Prob. 7TFQ Ch. 8.1 - Prob. 8TFQ Ch. 8.1 - Prob. 9TFQ Ch. 8.1 - Prob. 10TFQ

The triangle inequality: | a + b | ≤ | a | + | b | for any real numbers a and b. [Hint: For a real number x , what is x 2 ? ]

Solution Summary: The author explains that the triangle inequality is sqrtx2 for any real numbers a and b.

Videos

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Want to see the full answer?

Chapter 8 Solutions

The triangle inequality: | a + b | ≤ | a | + | b | for any real numbers a and b. [Hint: For a real number x , what is x 2 ? ]

Solution Summary: The author explains that the triangle inequality is sqrtx2 for any real numbers a and b.

Videos

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b. [Hint: For a real number x, what is x2?]

To prove: |x1+x2+....+xn|≤|x1|+|x2|+....+|xn| for any n≥1 and n real numbers x1,x2......xn

Want to see the full answer?

Chapter 8 Solutions

The triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.

[Hint: For a real number x, what is x2?]