5$5. The function
! (b
, xIation3]
(人 WIN
7/G) 和 xITationa] 60. Pr
1S called the 777cpe/,/rc/7oz. Prove that for no numberc exI
does lm 7(y) exist. (
Prove the limit statement. 司
56. 1 三了 i i 一從|) 三 人
lm 7G) =了 痢 lm7c-00 @ 1
27. lm /G) =了 論 lm7/c+人0
58. lim /G) =了 這 lmL/G)一句=0 2
$9. Suppose that 1 信人信導鹿導和 五
了
(a) Prove that 放工 > 0, then 7/(r) > 0 for aJY殼舉仙 62. Prove !
anterval ofthe form (c一十7 2and 有
HINT: Use an c,? argument, settinge 三也
圖 2.3 SOME LIMIT THEORENiS
As you probably gathered by Working througfh fhe Previous secfion, He
Tather tedious to apply the <, 8 definition of Jmmit time and time agamm- 是襄
general theorems, We can avoid some ofthis Tepetitive work. Of course,
themselves (at least the first ones) w征 have to be Proved bye,?
We begin by showing that ifa limit exists, ts unlque-
THEOREM 2.3.1 THE UNISUENESS GOFA LIMI
If lm /G)=Z and Jum7/G)三
2
pgoor We show 乙 二 籽 by proving that the 4