Question

求lim（x趋向于无穷）（1-1/x^2)^x的极限

Answer 1

由两个重要极限中的lim(1+1/x)^(x)=e(x趋于无穷）可对该式子进行变化

有lim(1-1/(x^2))^(x)=lim(1-1/(x^2))^(-x^2/x)

=lim((1-1/(x^2))^(-x^2))^(-1/x)

=lime^(-1/x)=1(x趋于无穷）