미분적분학 11판 솔루션 (Thomas 미적분학 (Calculus) 11e [Solutions])

CHAPTER 1 PRELIMINARIES
1.1 REAL NUMBERS AND THE REAL LINE 1. Executing long division, 2. Executing long division,
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2 9

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3 9

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3 11

8 9

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9 11

9 9

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11 11

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3. NT 〓 necessarily true, NNT 〓 Not necessarily true. Given: 2 [ x [ 6. a) NNT. 5 is a counter example. b) NT. 2 [ x [ 6 E 2 c 2 [ x c 2 [ 6 c 2 E 0 [ x c 2 [ 2. c) NT. 2 [ x [ 6 E 2/2 [ x/2 [ 6/2 E 1 [ x [ 3. d) NT. 2 [ x [ 6 E 1/2 ] 1/x ] 1/6 E 1/6 [ 1/x [ 1/2. e) NT. 2 [ x [ 6 E 1/2 ] 1/x ] 1/6 E 1/6 [ 1/x [ 1/2 E 6(1/6) [ 6(1/x) [ 6(1/2) E 1 [ 6/x [ 3. f) NT. 2 [ x [ 6 E x [ 6 E (x c 4) [ 2 and 2 [ x [ 6 E x ] 2 E cx [ c2 E cx + 4 [ 2 E c(x c 4) [ 2. The pair of inequalities (x c 4) [ 2 and c(x c 4) [ 2 E | x c 4 | [ 2. g) NT. 2 [ x [ 6 E c2 ] cx ] c6 E c6 [ cx [ c2. But c2 [ 2. So c6 [ cx [ c2 [ 2 or c6 [ cx [ 2. h) NT. 2 [ x [ 6 E c1(2) ] c1(x) [ c1(6) E c6 [ cx [ c2 4. NT 〓 necessarily tr…