x 趋向于0 求lim(cos1/x+2/sinx-1/ln(1+x))

题目

x 趋向于0 求lim(cos1/x+2/sinx-1/ln(1+x))

答案

用等价无穷小代换x趋于0时,sinx替换成x,ln(1+x)也替换成x极限变形为lim(cos1/x+2/x-1/x)=lim(cos1/x+1/x)=lim(xcos1/x+1)/xy=cos1/x是个有界函数,无穷小与有界函数的乘积趋于无穷小xcos1/x趋于0原极限=lim1/x左侧都...