作者LuisSantos ( )
看板trans_math
标题Re: [考古] 96中兴,化学系
时间Sat Jul 5 17:56:19 2008
※ 引述《SuzanneDuck (找回原来的自己..)》之铭言：
: 请问大家
: 96中兴 微积分的第一题
: ｌｉｍ [√(4x^2+5x+2)+2x]
: x→-∞
: 要怎麽算 @@
: 第一题就不会解 囧~~~~
: 请高手帮忙一下
: 谢谢
lim √(4x^2 + 5x + 2) + 2x
x→-∞
(√(4x^2 + 5x + 2) + 2x)(√(4x^2 + 5x + 2) - 2x)
= lim --------------------------------------------------
x→-∞ √(4x^2 + 5x + 2) - 2x
(4x^2 + 5x + 2) - (4x^2)
= lim ---------------------------
x→-∞ √(4x^2 + 5x + 2) - 2x
5x + 2
= lim ------------------------
x→-∞ √(4x^2 + 5x + 2) - 2x
(x)(5 + (2/x))
= lim ---------------------------------------
x→-∞ (|x|)(√(4 + (5/x) + (2/(x^2)))) - 2x
(x)(5 + (2/x))
= lim --------------------------------------
x→-∞ (-x)(√(4 + (5/x) + (2/(x^2)))) - 2x
(x)(5 + (2/x))
= lim --------------------------------------
x→-∞ (-x)(√(4 + (5/x) + (2/(x^2)))) - 2x
5 + (2/x)
= lim -------------------------------------
x→-∞ (-1)(√(4 + (5/x) + (2/(x^2)))) - 2
5 + 0
= -------------------------
(-1)(√(4 + 0 + 0) - 2)
5 -5
= -------- = ----
-2 - 2 4
--
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◆ From: 61.66.173.21
1F：推 SuzanneDuck:谢谢你^^ 61.223.214.130 07/06 10:18