lim[(x,y)->(0,0)][(x^3+x^5)/(x²+y²)极限是

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lim[(x,y)->(0,0)][(x^3+x^5)/(x²+y²)极限是
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lim[(x,y)->(0,0)][(x^3+x^5)/(x²+y²)极限是
lim[(x,y)->(0,0)][(x^3+x^5)/(x²+y²)极限是

lim[(x,y)->(0,0)][(x^3+x^5)/(x²+y²)极限是
(x,y)→(0,0)
lim (x^3+x^5) / (x^2+y^2)
用极坐标替换
x=ρcosθ,y=ρsinθ
=lim(ρ→0) (ρ^3cos^3θ+ρ^5cos^5θ) / ρ^2(sin^2θ+cos^2θ)
=lim (ρ^3cos^3θ+ρ^5cos^5θ) / ρ^2
=lim ρcos^3θ+ρ^3cos^5θ
因为cos^3θ,cos^5θ都有界
故,
lim (x^3+x^5) / (x^2+y^2)=0
有不懂欢迎追问

假设（x,y）沿着y=x的路径趋于（0,0），那么lim[(x,y)->(0,0)][(x^3+x^5)/(x²+y²)]=lim[x->0][(x^3+x^5)/(x²+x²)]=0。
也可以假定为其他路径趋于（0,0），极限结果应是一样的

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