Re: [微分] 兩題
※ 引述《xx52002 (長門有希好萌(′▽‵))》之銘言：
: (1)Prove that x-(1/6)x^3 < sinx for all x屬於(0,∞)
3
x
令F(x)= sinx-x+ ---
6
1 2
F'(x) =cosx - 1 + --- x = 0 => x = 0
2
F(x)=0為極小值
F(x) > F(0) = 0
3
x
=> sinx - x + --- > 0
6
3
x
=> x - --- < sinx (Q.E.D.)
6
: (2)Let f and g be differential functions such that
: f'(x) = -g(x), g'(x) = f(x) for all x
: Suppose that f(a)=1, g(a)=0, prove that f^2(x)+g^2(x)=1
: 拜託各位了 @@
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※ 編輯: GayerDior 來自: 61.229.150.204 (12/08 00:49)
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