(a) To list: All the symmetries of the given rectangle.

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Answer 1

Question

Chapter 11, Problem 39E

To determine

(a)

To list:

All the symmetries of the given rectangle.

To determine

(b)

To list:

All the symmetries of the parallelogram.

To determine

(c)

To list:

All the symmetries of the trapezium.

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Keity x२ 1. (i) Identify which of the following subsets of R2 are open and which are not. (a) A = (2,4) x (1, 2), (b) B = (2,4) x {1,2}, (c) C = (2,4) x R. Provide a sketch and a brief explanation to each of your answers. [6 Marks] (ii) Give an example of a bounded set in R2 which is not open. [2 Marks] (iii) Give an example of an open set in R2 which is not bounded. [2 Marks

2. (i) Which of the following statements are true? Construct coun- terexamples for those that are false. (a) sequence. Every bounded sequence (x(n)) nEN C RN has a convergent sub- (b) (c) (d) Every sequence (x(n)) nEN C RN has a convergent subsequence. Every convergent sequence (x(n)) nEN C RN is bounded. Every bounded sequence (x(n)) EN CRN converges. nЄN (e) If a sequence (xn)nEN C RN has a convergent subsequence, then (xn)nEN is convergent. [10 Marks] (ii) Give an example of a sequence (x(n))nEN CR2 which is located on the parabola x2 = x², contains infinitely many different points and converges to the limit x = (2,4). [5 Marks]

2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1 Mark] (ii) Prove that if a set ECR2 is closed then every convergent sequence (x(n))nen in E has its limit in E, that is (x(n)) CE and x() x x = E. [5 Marks] (iii) which is located on the parabola x2 = = x x4, contains a subsequence that Give an example of an unbounded sequence (r(n)) nEN CR2 (2, 16) and such that x(i) converges to the limit x = (2, 16) and such that x(i) # x() for any i j. [4 Marks

Answer 2

Question

Chapter 11, Problem 39E

To determine

(a)

To list:

All the symmetries of the given rectangle.

To determine

(b)

To list:

All the symmetries of the parallelogram.

To determine

(c)

To list:

All the symmetries of the trapezium.

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Answer 3

Question

Chapter 11, Problem 39E

To determine

(a)

To list:

All the symmetries of the given rectangle.

To determine

(b)

To list:

All the symmetries of the parallelogram.

To determine

(c)

To list:

All the symmetries of the trapezium.

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Answer 4

Question

Chapter 11, Problem 39E

To determine

(a)

To list:

All the symmetries of the given rectangle.

To determine

(b)

To list:

All the symmetries of the parallelogram.

To determine

(c)

To list:

All the symmetries of the trapezium.

Expert Solution & Answer

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Answer 5

Chapter 11, Problem 39E

To determine

(a)

To list:

All the symmetries of the given rectangle.

To determine

(b)

To list:

All the symmetries of the parallelogram.

To determine

(c)

To list:

All the symmetries of the trapezium.

Answer 6

Chapter 11, Problem 39E

To determine

(a)

To list:

All the symmetries of the given rectangle.

Answer 7

Chapter 11, Problem 39E

To determine

(a)

To list:

All the symmetries of the given rectangle.

Answer 8

To determine

(b)

To list:

All the symmetries of the parallelogram.

Answer 9

To determine

(b)

To list:

All the symmetries of the parallelogram.

Answer 10

To determine

(c)

To list:

All the symmetries of the trapezium.

Answer 11

To determine

(c)

To list:

All the symmetries of the trapezium.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 11 - In Fig.1135_, indicate which point is the image of...Ch. 11 - Prob. 2E Ch. 11 - Prob. 3E Ch. 11 - In Fig. 11-38, P is the image of P under a...Ch. 11 - In Fig.11-39, l is the axis of reflection. a.Find...Ch. 11 - In Fig. 11-40, l is the axis of reflection. a....Ch. 11 - Prob. 7E Ch. 11 - In Fig 11-42, P is the image of P under a...Ch. 11 - In Fig. 11-43, P is image of P under a reflection....Ch. 11 - Prob. 10E

(a) To list: All the symmetries of the given rectangle.

Solution Summary: The author explains that the rectangle has two reflection and rotation symmetries.

(a)

To list:

All the symmetries of the given rectangle.

(b)

To list:

All the symmetries of the parallelogram.

(c)

To list:

All the symmetries of the trapezium.

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Chapter 11 Solutions

(a) To list: All the symmetries of the given rectangle.

Solution Summary: The author explains that the rectangle has two reflection and rotation symmetries.

(a) To list: All the symmetries of the given rectangle.

(b) To list: All the symmetries of the parallelogram.

(c) To list: All the symmetries of the trapezium.

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Chapter 11 Solutions

(a)

To list:

All the symmetries of the given rectangle.

(b)

To list:

All the symmetries of the parallelogram.

(c)

To list:

All the symmetries of the trapezium.