Re: [考古]
※ 引述《lenta (若無其事)》之銘言：
: 1. 2 2 2
: x,y,z are positive number find the minimum of (x +1)(y +1)(z +1)
: ------------------
: xyz
xyz除進去
(x+1/x)(y+1/y)(z+1/z)
x+1/x
----- => √1=>1
2
(x+1/x)=>2
(x+1/x)(y+1/y)(z+1/z)=>8
: 2.
: calculate
: 2 2 2
: S (5+x y)dS,where C is the upper half of the unit circle x +y = 1
: C
x=rcosθ
y=rsinθ
π1
∫∫ (5+(rcosθ)^2rsinθ)rdrdθ
0 0
: 3.
: find an equation of the tangent plane to the graph of
: 2 2 2
: x -4y +z =16 at(2,-1,4)
▽f(x,y,z)=(2x,-8y,2z)
代(2,-1,4) = (4,8,8)
(1,2,2)(x-2,y+1,z-4)=0
: 麻煩了@@
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