(x,y)趋于(0,0),求极限(x^3+y^3)/(x^2+y^2)类似地,求x趋近于0,y趋于0时(x^3-y^3)/(x^2+y^2)的极限,如果方法差不多就不用讲了.详解,

Question

(x,y)趋于(0,0),求极限(x^3+y^3)/(x^2+y^2)
类似地,求x趋近于0,y趋于0时(x^3-y^3)/(x^2+y^2)的极限,如果方法差不多就不用讲了.详解,

Answer 1

(x,y)趋于(0,0),求极限(x³+y³)/(x²+y²)
设动点P(x,y)沿着直线y=kx(k∈R)趣近(0,0),那么：
x➔0,y=kx➔0lim[(x³+y³)/(x²+y²)]=x➔0,y=kx➔0lim[(x³+k³x³)/(x²+k²y²)]
=x➔0,y=kx➔0lim[x(1+k³)/(1+k²)]=0