l = \(\lim\limits_{x\to 0}(\frac1{x^2}-\frac{e^x}{e^x-1})^2\)
= \(\lim\limits_{x\to 0}(\frac1{x^2}-\frac{e^x-1-x^2e^x}{x^2(e^x-1)})^2\)
= \((\lim\limits_{x\to 0}\frac{e^x-1-x^2e^x}{x^2(e^x-1)})^2\) (0/0 type)
= \((\lim\limits_{x\to 0}\frac{e^x-x^2e^x-2xe^x}{x^2e^x+2xe^x-2x})^2\)(By applying D.L.H. Rule)
= \((\frac10)^2\) = ∞
\(\therefore\) \(\frac1l=\frac1\infty\) = 0
