2 LIMITS

CHAPTER 2LIMITSGROUP WORK 3: The Squeeze Theoremsin xThis exercise gives an informal graphical way to show that lim = 1. A more careful geometric argumentx→0 xisgiveninSection3.4.Answers:1., 2.y3. For x > 0, sin x < x ⇒ sin x < 1.x1 y=xy=sin xFor x < 0, sin x > x ⇒ sin x < 1y=x-x#/6x(reversing the second inequality becausex < 0)._1 01 x4. f (x) = 1 − x265. The Squeeze Theorem now givessin xlim = 1._1x→0 xHOMEWORK PROBLEMSCore Exercises: 1, 6, 15, 18, 31, 37, 46, 49, 58Sample Assignment: 1, 6, 10, 15, 18, 31, 34, 35, 37, 42, 46, 49, 52, 58, 61Exercise D A N G1 ×6 ×10 × ×15 ×18 ×31 × × × ×34 × ×35 ×Exercise D A N G37 × ×42 ×46 × × ×49 ×52 × ×58 ×61 ×54