m(sinx/x)=1(x->0) m(1 + 1/x)^x=e (x->无穷大) 怎么证出来的?*_*
热心网友
1. x==0时： lim(sinx/x) = lim[(sinx)'/(x)'](根据罗必塔定理) =limcosx=12. 令y=1/x，则，x==无穷大时,y==0x==无穷大时, lim(1 + 1/x)^x = lim e^[x*ln(1+ 1/x)]= e^{lim[x*ln(1+ 1/x)]} = e^{lim[ln(1+y)]/y}= e^{lim[ln(1+y)]'/[y]'} ,(根据罗必塔定理)= e^{lim[1/(1+y)]}= e^1= e