作者LuisSantos (^______^)
看板trans_math
标题Re: [积分]
时间Tue Mar 6 18:52:33 2007
※ 引述《king911015 (早已放弃爱上你)》之铭言：
: x
: x∫ e^t^2 dt
: lim 0
: x→0 ---------------- =?
: 1 - e^x^2
x
(x)(∫ e^(t^2) dt)
0
lim --------------------
x→0 1 - e^(x^2)
x
∫ e^(t^2) dt + (x)(e^(x^2))
0
= lim ---------------------------------
x→0 (-2x)(e^(x^2))
e^(x^2) + (2x)(e^(x^2)) + (e^(x^2))
= lim --------------------------------------
x→0 (-2)(e^(x^2)) - (2x)(2x)(e^(x^2))
1 + 0 + 1 2
= ----------- = ----- = -1
-2 - 0 -2
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