114 復興高中
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Re: 114 復興高中
第 10 題
作 GD 垂直 BC 於 D，GE 垂直 AC 於 E
6 = GD + GE = (1/3)(AC + BC)
AC + BC = 18
又 AC^2 + BC^2 = 15^2
可求出 △ABC = (1/2) * AC * BC = 99/4
作 GD 垂直 BC 於 D，GE 垂直 AC 於 E
6 = GD + GE = (1/3)(AC + BC)
AC + BC = 18
又 AC^2 + BC^2 = 15^2
可求出 △ABC = (1/2) * AC * BC = 99/4
Re: 114 復興高中
第 4 題
y = (x - x^3)/(1 + 2x^2 + x^4)
= x(1 - x^2)/(1 + x^2)^2
= (1/2) * [(2x)/(1 + x^2)] * [(1 - x^2)/(1 + x^2)]
令 x = tanθ，tan2θ = (2x)/(1 - x^2)
y = (1/2)sin2θcos2θ = (1/4)sin4θ
當 sin4θ = 1 時，y 有最大值 1/4
y = (x - x^3)/(1 + 2x^2 + x^4)
= x(1 - x^2)/(1 + x^2)^2
= (1/2) * [(2x)/(1 + x^2)] * [(1 - x^2)/(1 + x^2)]
令 x = tanθ，tan2θ = (2x)/(1 - x^2)
y = (1/2)sin2θcos2θ = (1/4)sin4θ
當 sin4θ = 1 時，y 有最大值 1/4