当x趋近于无穷时 lim(x^2/x^2-1)^x

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当x趋近于无穷时 lim(x^2/x^2-1)^x
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当x趋近于无穷时 lim(x^2/x^2-1)^x
当x趋近于无穷时 lim(x^2/x^2-1)^x

当x趋近于无穷时 lim(x^2/x^2-1)^x
答:
原式
=lim x->∞ (1+1/(x^2-1))^x
=lim x->∞ (1+1/(x^2-1))^((x^2-1)*(x/(x^2-1))
=lim x->∞ e^(x/(x^2-1))
=lim x->∞ e^0
=1

lim[1/(1-1/x^2)]^x
=lim(1-1/x^2)^(-x)
x^2=X
=√lim(1-1/X)^(-X)
-1/X=Y
-X=1/Y
lim(1+Y)^(1/Y)
Y→0
√e