[微積] 級數證明.雙變數極值
各位版友午安:
A_n+1
1)Let A_n >0 for all "(n屬於N)" ,and lim(───)=λ.Show that if λ<1,then
A_n
∞
Σ A_n converges.
n=1
2)Find the volume of the solid bounded above by the surface z=3-(√x^2+ y^2),
below by the xy-plane, and on the sides by the cylinder x^2+y^2=3x.
3)Find the absolute extreme values taken on by f(x,y)=x^2+9y^2+x-(√3)y.
x^2
on the closed region enclosed by the ellipse ─── + y^2 = 1.
9
第一題證明,有點類似等比級數公比小於1那種,但還是不知從何證起?
第二題體積積分比較沒想法,想問問版友給予提示
第三題多變數求極值
令
x^2
────+y^2=1=g(x,y)
9
利用▽f=λ▽p來解
2
(2x+1)=λ(── x)-----(a)
9
18y-√3=λ(2y)------(b)
x^2
─── + y^2=1--------(c)
9
得(a)(b)(c)三式,每次解到這都不知道要從何下手
想參考版友們的作法
謝謝
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