求证：lim(1+1/x）^x的极限等于e

Question

求证：lim(1+1/x）^x的极限等于e

Answer 1

当(x→∞) lim(1+1/x）^x=lime^xln(1+1/x) 因为x→∞,所以1\x→0.在用等价无穷小代换ln(1+1/x) =1\x所以原式就变成了当(x→∞) lim(1+1/x）^x=lime^xln(1+1/x) =lime^x*1/x=e