lim(x趋于0) x^2 * e^(1/x^2)
=lim(x趋于0) e^(1/x^2) / (1/x^2) x趋于0的时候,分子分母都趋于0,用洛必达法则同时求导
=lim(x趋于0) e^(1/x^2) *(1/x^2)' / (1/x^2)'
=lim(x趋于0) e^(1/x^2)
那么很显然x趋于0时,1/x^2趋于正无穷,所以e^(1/x^2)趋于正无穷,
即原极限趋于正无穷