Calculus 11e sol george thomas (1)

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Calculus 11e sol george thomas (1)

CHAPTER 1 PRELIMINARIES1.1 REAL NUMBERS AND THE REAL LINE1.Executing long division, Ậ = 0.Ĩ, 5 = 0.2. 5 = 0.3, * = 0.8.1 = 0.92.Executing long divisio

Calculus 11e sol george thomas (1) on, ĩỳ = 0.09, Pf = 0.18, jy = 0.27, ^y = 0.81, ỳỳ = 0.993.NT = necessarily true, NNT = Not necessarily true. Given: 2 < X < 6.a)NNT. 5 is a counter e

xample.b)NT. 22-20 I < X < 3.d)NT. 2 < X <6=>1/2 > 1/x > 1/6=> 1/6 < 1/x < 1/2.c)NT.2 Calculus 11e sol george thomas (1)

1/2 > l/x> 1/6=> l/6< l/x< 1/2 => 6(1/6) <6(l/x)<6(l/2)=>1 <6/x<3.f)NT. 2 < X < 6=>X < 6 => (X - 4) < 2 and 2 < X < 6 => X > 2=>-X < -2=>-X+4 < 2=> -(

Calculus 11e sol george thomas (1)

x - 4) < 2.The pair of inequalities (x - 4) < 2 and - (x -4) <2 => I X — 4 I < 2.g)NT. 2 < X < 6 => -2 > -X > -6 => -6 < -X < -2. But -2 < 2. So -6 <

CHAPTER 1 PRELIMINARIES1.1 REAL NUMBERS AND THE REAL LINE1.Executing long division, Ậ = 0.Ĩ, 5 = 0.2. 5 = 0.3, * = 0.8.1 = 0.92.Executing long divisio

Calculus 11e sol george thomas (1) 1 -l+54

4 < y < 6 y > 4.d)NT. From a), -1 < y — 5 < 1. => 4 < y < 6 =e- y < 6.c) NT.-Ky-5<1 =>-1 + 1 0(I/2X-1 + 5) < Calculus 11e sol george thomas (1)

(l/2Xy - 5 + 5)< (1/2X1 +5) =>2 1/4 > 1/y > 1/61/6 < 1/y < 1/4.h)NT.-Iy-5>-1 => y>4 => -y<-4 => -y + 5

Calculus 11e sol george thomas (1)

> -(y-5) y - 5 < I. The pair of inequalities -(y — 5) < 1 and (y — 5) < I => I y — 5 I < I.5.-2x >4 => X < -26.8 - 3x > 5 =

CHAPTER 1 PRELIMINARIES1.1 REAL NUMBERS AND THE REAL LINE1.Executing long division, Ậ = 0.Ĩ, 5 = 0.2. 5 = 0.3, * = 0.8.1 = 0.92.Executing long divisio

Calculus 11e sol george thomas (1) X or - ị > X10.^£<25^ => 12 - 2x < 12x - 16=> 28 < 14x => 2 < X2 Chapter I Preliminaries11.3 (X - 2) < Ị (X - 6) => 12(x - 2) < 5(x - 6)=> 12x - 24 <

5x-30 => 7x < -6 or X < — 712.- ip <=> —(4x + 20) < 24 + 6x Calculus 11e sol george thomas (1)

CHAPTER 1 PRELIMINARIES1.1 REAL NUMBERS AND THE REAL LINE1.Executing long division, Ậ = 0.Ĩ, 5 = 0.2. 5 = 0.3, * = 0.8.1 = 0.92.Executing long divisio