迫近定理的數

1)lim x→0 (3x / sinx - x)
3lim x→0 (x /sinx-x)
3lim x→0 (1/sinx/x - 1)
3lim x→0 (1/1-1)
therefore, the limit is undefined

2)lim x→0 (1 - cos mx / x^2)
m^2lim x→0 (sin^2mx)(1-cosmx)/(sin^2mx)(m^2x^2)
m^2lim x→0 (sinmx/mx)^2(1-cosmx)/(sin^2mx)
m^2lim x→0 (sinmx/mx)^2(1-cosmx)/(1-cos^2mx)
m^2lim x→0 (sinmx/mx)^2(1-cosmx)/(1-cosmx)(1+cosmx) = m^2/2

3)lim x→1【(x-1)^2 sin (x-1) 】
lim x→1 (1-1)^2 sin(1-1) = 0

4)lim x→ 兀 / 2【 ( 2x - 兀 )^2 (tan^2x + 1)】
lim x→ 兀 / 2 【 ( 2x - 兀 )^2 sec^2】
lim x→ 兀 / 2 【 ( 2x - 兀 )^2 1/cos^2】
lim x→ 兀 / 2 【 ( 2x - 兀 ) /sin(兀 / 2-x)】^2
-4lim x→ 兀 / 2 【 (兀 /2-x) /sin(兀 / 2-x)】^2 = -4

2007-08-26 21:12:23 補充：
本人在這一類數方面還未完全掌握,所以不知是否準確

lim x →?............係指 x 最終會等於接近於"?"的數
所以當..lim x→0
3x / sinx - x→0
-------------------------------------------
當..lim x→0
1 - cos mx / x^2→負無限
-----------------------------------------------
當..lim x→1
(x-1)^2 sin (x-1) →0
-------------------------------------------------
當...lim x→ 兀 / 2
( 2x - 兀 )^2 (tan^2x + 1)→0

1.x=0
2.x=0
3.x=0
4.x=0