미분적분학 3판 솔루션 Robert T. 스미스 (Smith) CALCULUS STUDENT SOLUTION MANUAL 2007 SMITH 3RD EDITION

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