原式=lim[e^(sin x/3)-1]/(sin x/3)*(sin x/3)/x 将它化为两部分乘积,可分别求极限=1×1/3=1/3也可用等价无穷小:x=3*x/3与3(sin x/3)等价原式=lim[e^(sin x/3)-1]/[3(sin x/3)]=1/3 lim[e^(sin x/3)-1]/(sin x/3)=1/3注意:等价无穷小一定在乘除项中代换,在加减项中代换可能错误