求极限lim<sub>x→0<sub>[1/x-1/(e<sup>x</sup>-1)]．

求极限lim_{x→0_{[1/x-1/(e^x-1)]．}}

求极限lim_{x→0_{[1/x-1/(e^x-1)]．
【正确答案】：lim_x→0[1/x-1/(e^x-1)] =lim_x→0{(e^x-1-x)/[x(e^x-1)]} =lim_x→0[(e^x-1-x)/x²] =lim_x→0[(e^x-1)/2x-1/2]}}

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