x趋向无穷时,求lim e^-x乘以(1+1/x)^(x^2),求方法,

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x趋向无穷时,求lim e^-x乘以(1+1/x)^(x^2),求方法,
答案好像是e^1/2还是e^-1/2的样子

lime^-x乘以(1+1/x)^(x^2),
=lim1/e^x乘以(1+1/x)^(x*x),
=lim1/(1+1/x)^x乘以(1+1/x)^(x*x),
=lim(1+1/x)^[x*(x-1)]
=lime^(x-1)
=∞,

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