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Hex - Sketch Solutions for Exercises in the Main Text of A...

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Sketch Solutions for Exercises in the Main Text of A First Look at Vectors T. W. K¨orner 1
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2 Introduction Here are what I believe to be sketch solutions to the bulk of exercises in the main text the book (i.e. those not in the “Further Exercises”). I have written in haste in the hope that others will help me correct at leisure. I am sure that they are stuffed with errors ranging from the T E Xtual through to the arithmetical and not excluding serious math- ematical mistakes. I would appreciate the opportunity to correct at least some of these problems. Please tell me of any errors, unbridge- able gaps, misnumberings etc. I welcome suggestions for additions. ALL COMMENTS GRATEFULLY RECEIVED. If you can, please use L A T E X2 ε or its relatives for mathematics. If not, please use plain text. My e-mail is [email protected] . You may safely assume that I am both lazy and stupid so that a message saying ‘Presumably you have already realised the mistake in Exercise Z is less useful than one which says ‘I think you have made a mistake in Exercise Z because you have have assumed that the sum is necessarily larger than the integral. One way round this problem is to assume that f is decreasing.’ When I was young, I used to be surprised when the answer in the back of the book was wrong. I could not believe that the wise and gifted people who wrote textbooks could possibly make mistakes. I am no longer surprised. It may be easiest to navigate this document by using the table of contents which follow on the next few pages. To avoid disappointment, observe that those exercises marked have no solution given.
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3 Contents Introduction 2 Exercise 1.1.2 13 Exercise 1.2.1 14 Exercise 1.2.2 15 Exercise 1.2.3 16 Exercise 1.2.5 17 Exercise 1.2.6 18 Exercise 1.2.7 19 Exercise 1.2.8 20 Exercise 1.2.9 20 Exercise 1.2.10 21 Exercise 1.3.5 22 Exercise 1.3.9 23 Exercise 1.3.10 25 Exercise 1.4.3 26 Exercise 2.1.3 27 Exercise 2.1.4 28 Exercise 2.1.6 28 Exercise 2.1.7 28 Exercise 2.1.9 29 Exercise 2.2.4 29 Exercise 2.2.5 29 Exercise 2.2.8 30 Exercise 2.2.10 31 Exercise 2.3.3 32 Exercise 2.3.4 32 Exercise 2.3.11 33 Exercise 2.3.12 34 Exercise 2.3.13 35 Exercise 2.3.14 36 Exercise 2.3.16 37 Exercise 2.3.17 38 Exercise 2.3.18 39 Exercise 2.4.1 40 Exercise 2.4.2 41 Exercise 2.4.4 41 Exercise 2.4.6 42 Exercise 2.4.9 43 Exercise 2.4.10 44 Exercise 2.4.11 45 Exercise 2.4.12 46 Exercise 3.2.1 47 Exercise 3.3.4 48
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4 Exercise 3.3.6 49 Exercise 3.3.9 50 Exercise 3.3.10 52 Exercise 3.3.12 53 Exercise 3.3.13 54 Exercise 3.3.14 55 Exercise 3.4.5 56 Exercise 3.4.7 57 Exercise 3.5.1 58 Exercise 3.5.2 59 Exercise 4.1.1 60 Exercise 4.1.2 61 Exercise 4.1.3 62 Exercise 4.2.1 63 Exercise 4.2.2 64 Exercise 4.2.3 64 Exercise 4.3.2 65 Exercise 4.3.3 66 Exercise 4.3.10 67 Exercise 4.3.13 68 Exercise 4.3.14 69 Exercise 4.3.15 70 Exercise 4.3.16 70 Exercise 4.4.1 71 Exercise 4.4.4 72 Exercise 4.4.6 73 Exercise 4.4.7 74 Exercise 4.4.8 75 Exercise 4.4.9 76 Exercise 4.5.1 78 Exercise 4.5.3 79 Exercise 4.5.3 80 Exercise 4.5.5 81 Exercise 4.5.6 82 Exercise 4.5.7 83 Exercise 4.5.8 84 Exercise 4.5.10 85 Exercise 4.5.13 86 Exercise 4.5.14 87 Exercise 4.5.15 88 Exercise 4.5.16 89 Exercise 4.5.17 90 Exercise 5.1.1 91 Exercise 5.1.2 91 Exercise 5.2.7 92
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5 Exercise 5.2.8
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