lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2y2

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lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2y2lim(x,y)→(0,0)(1-cos(x

lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2y2
lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2
lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2y2

lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2lim(x,y)→(0,0)(1-cos(x2+y2))/(x2+y2)x2y2
=lim(x,y)→(0,0) (1/2)·(x2+y2)²/(x2+y2)x2y2
=lim(x,y)→(0,0) (1/2)·(x2+y2)/x2y2
→∞

利用极坐标替换即可