作者LuisSantos ( )
看板trans_math
标题Re: [考古] 台大92c 第E题
时间Thu Jul 10 22:46:54 2008
※ 引述《vivaonly (viva)》之铭言：
: x
: *设连续函数f满足f(x)= ∫f(t)dt+2,则f(x)=?
: 0
: 我用微积分第一基本定理求出 f'(x)=f(x) 然後...就卡住了
: 请大大帮我解答谢谢
0
f(0) = ∫ f(t) dt + 2 = 0 + 2 = 2
0
f'(x) = f(x)
d(f(x))
--------- = f(x)
dx
d(f(x))
--------- = dx
f(x)
=> ln|f(x)| = x + c_1 = ln(e^(x + c_1))
=> f(x) = ±e^(x+c_1) = (±e^(c_1))(e^x) = (c)(e^x)
=> f(0) = 2 => 2 = c
f(x) = (2)(e^x)
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