※ 引述《vivaonly (viva)》之銘言：
: x
: *設連續函數f滿足f(x)= ∫f(t)dt+2,則f(x)=?
: 0
: 我用微積分第一基本定理求出 f'(x)=f(x) 然後...就卡住了
: 請大大幫我解答謝謝
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)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.66.173.21