※ 引述《wenex (wenex)》之銘言：
: 1. f(x)=e^(x^2) 則f^(100)(0)=______
∞
∵ e^x = Σ x^n/n!
n=0
∞
∴ e^(x^2) = Σ x^(2n)/n!
n=0
∞
= Σ [f^(k)(0)/k!]x^k
k=0
=> k = 2n and f^(k)(0)/k! = 1/n!
=> let k = 100 , n = 50
=> f^(100)(0)/100! = 1/50!
=> f^(100)(0) = 100!/50!
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→ Jesusboo:keyboard就是男人那隻翹起的意思 11/29 17:21
推 Beef:那叫做keychord 11/29 17:22
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