Re: [考古] 台大95C(4)
※ 引述《thirdface (第三張臉)》之銘言:
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: 設 f(x)= ∫ f(t)dt + 3 ,求f(x)
: x
x
f(x) = -∫f(t)dt + 3 --(*)
0
根據微積分基本定理
f'(x) = -f(x)
=> df/dx = -f
=> df/f = -dx
對兩邊積分=> ln|f| = -x + C
(i) => f(x) = e^(-x+C)
for x=0
f(0) = e^C = 3 => C=ln3
so f(x) = e^(-x+ln3) = e^(-x) * e^(ln3) = 3e^(-x)
(ii) => f(x) = -e^(-x+C)
for x=0
f(0) = -e^C = 3 => C=-ln3
so f(x) = -e^(-x-ln3) = -e^(-x) * e^(-ln3) = 3e^(-x)
from(i)and(ii) , f(x) = 3e^(-x)
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07/02 01:49, , 1F
07/02 01:49, 1F
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