{y+2z=1 2x-3y-4z=-3 3x-2z=5解方程{y+2z=1 2x-3y-4z=-3 3x-2z=5

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{y+2z=1 2x-3y-4z=-3 3x-2z=5解方程{y+2z=1 2x-3y-4z=-3 3x-2z=5
{y+2z=1 2x-3y-4z=-3 3x-2z=5
解方程{y+2z=1 2x-3y-4z=-3 3x-2z=5

{y+2z=1 2x-3y-4z=-3 3x-2z=5解方程{y+2z=1 2x-3y-4z=-3 3x-2z=5
y+2z=1 (1)
2x-3y-4z=-3 (2)
3x-2z=5 (3)
由(1)
y=1-2z
由(3)
x=(5+2z)/3
代入(2)
(10+4z)/3-3(1-2z)-4z=-3
10+4z-9+18z-12z=-9
10z=-10
z=-1
y=1-2z=3
x=1

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y=(a^x+b^x)^(3/x)
lny=3/x*ln(a^x+b^x)=3ln(a^x+b^x)/x
这是∞/∞,可以用洛必达法则
分子求导=[3/(a^x+b^x)]*(a^x*lna+b^x*lnb)
分母求导=1
所以=3*(a^x*lna+b^x*lnb)/(a^x+b^x)
若|a|<|b|
则上下除以b^x
=3[(a/b)^x*lna+lnb]/[(a/b)^x+1]
此时(a/b)^x趋于0
所以lny极限=3lnb
同理
若 |a|>|b|，则lny极限=3lna
综上
|a|<|b|,极限=e^(3lnb)
|b|<|a|,极限=e^(3lna)

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