高数题，求极限？
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lim(x,y->∞,a)(1+1/(xy))^(x²/(x+y))
=lim(x,y->∞,a)(1+1/(xy))^[xy(x/y)/(x+y)]
=lim(x,y->∞,a)e^[(x/y)/(x+y)]
=lim(x,y->∞,a)e^[(1/y(1+y/x)]
=lim(x,y->∞,a)e^(1/y)
=e^(1/a)
=lim(x,y->∞,a)(1+1/(xy))^[xy(x/y)/(x+y)]
=lim(x,y->∞,a)e^[(x/y)/(x+y)]
=lim(x,y->∞,a)e^[(1/y(1+y/x)]
=lim(x,y->∞,a)e^(1/y)
=e^(1/a)
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