Re: [微積] 請教台大102微積分一題
※ 引述《kan81314 (King And Natasha)》之銘言:
: ※ 引述《aaacheng000 (阿誠~)》之銘言:
: : http://exam.lib.ntu.edu.tw/sites/default/files/exam/graduate/102/102477.pdf
: 順便請教第六題的(b)
: 感恩!!
x
[I_n(x)]^(1/n) = (2/π)∫√[1-t^2] dt
1
= (2/π)[π/4 + (1/2)arcsin(x) + (1/2)x√(1-x^2)]
x = 1 - t/n^α α>0
當n -> ∞
I_n(x) ~ {(2/π)[π/2 - (t/n^α)√(1-(1-βt/n^α))]}^n β為0~1的某數
~ {1 - (2t/πn^α)√(2βt/n^α)}^n
如果極限不為0或1
α = 2/3
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