作者LuisSantos (^______^)
看板trans_math
标题Re: [积分]
时间Mon Feb 19 19:01:23 2007
※ 引述《king911015 (早已放弃爱上你)》之铭言：
: x
: 设连续函数f满足f(x) = ∫ f(t)dt + 2 ，则f(x) =__________
: 0
x
f(x) = ∫ f(t) dt + 2
0
d(f(x))
--------- = f(x)
dx
d(f(x))
--------- = dx
f(x)
ln|f(x)| = x + c_1
|f(x)| = e^(x+c_1) = (e^(c_1))(e^x)
f(x) = (e^(c_1))(e^x) , -(e^(c_1))(e^x)
f(x) = (c)(e^x) , (c = e^(c_1) , -(e^(c_1)))
0
f(0) = ∫ f(t) + 2 = 0 + 2 = 2
0
将f(0) = 2代入f(x) = (c)(e^x) 得
2 = (c)(e^0) = c => c = 2
f(x) = (2)(e^x)
: x^2
: ∫ (e^t^2 +4)dt
: 0
: Find lim --------------------- = ?
: x→0 (sinX)^2
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