推 Jasy:right 218.187.11.143 05/08
推 beatitude:ya 218.167.179.21 05/08
※ 引述《Jasy (面對現實)》之銘言：
: 1.Suppose that f is a conti function which satisfies the intergral equation
: x f(t)
: f(x)=2 + S ------------ dt, x>=0 then f(1)=?
: 0 (t+2)(t+3)
f(x) df f(x)
f'(x) = ------------- ---- = -----------
(x+2)(x+3) dx (x+2)(x+3)
x + 2
lnf(x) = ln------- + c
x + 3
x + 2
-> f(x) = a(-------) f(0) = 2 -> a = 3
x + 3
9
-> f(1) = ---
4
有錯請指正
: -x^2(t^2+1)
: x -t^2 2 1 e
: 2.If f(x)={S e dt} , g(x)=S ------------- dt, then
: 0 0 2
: t +1
: (1) Show that g'(x)+f'(x)=0 for all of x
: (2) Use (1) to show that g(x)+f(x)=π/4
: ∞ -t^2 dt
: (3) Use (2) to prove that S e = √π/2
: 0
--
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