为自己加油

极限lim_x→0=____．

1/2 分析：lim_x→0[1/x-1/(e^x-1)]=lim_x→0-x²/(1+x²) =lim_x→0(e^x-1-x)′/(xe^x)=lim_x→0(e^x-1)/(e^x+xe^x-1) =lim_x→0(e^x-1)′/(e^x+xe^x-1)′=lim_x→0[e^x(2e^x+xe^x)=1/2