问题及解答

求下列极限.

\[
\lim_{x\rightarrow 0}\Bigl(\frac{1}{x}-\frac{1}{e^x-1}\Bigr)
\]

\[
\lim_{x\rightarrow 0}\Bigl(\frac{1}{x}-\frac{1}{e^x-1}\Bigr)=​\lim_{x\rightarrow 0}\frac{e^x-1-x}{x(e^x-1)}=​\lim_{x\rightarrow 0}\frac{e^x-1-x}{x^2}=​\lim_{x\rightarrow 0}\frac{e^x-1}{2x}=​\lim_{x\rightarrow 0}\frac{x}{2x}=\frac{1}{2}.
\]