lim(x趋向无穷大)[1-(2/x)]^(x+2)怎么计算请写出详细过程

Question

lim(x趋向无穷大)[1-(2/x)]^(x+2)怎么计算 请写出详细过程

Answer 1

令y=[1-(2/x)]^(x+2)lny=ln{[1-(2/x)]^(x+2)}=(x+2)ln[1-2/x]=ln(1-2/x)/[1/(x+2)]当x->无穷分子1-2/x->1,ln(1-2/x)->0分母1/(x+2)->00除0,得用洛必达法则分子求导=[1/(1-2/x)]*2/x^2=2/(x^2-2x)分母求导=-1/(x+2)^2...