当x趋近于无穷时 lim(x^2/x^2-1)^x

题目

当x趋近于无穷时 lim(x^2/x^2-1)^x

答案

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