\(\lim\limits_{x \to 0} \frac{e^x+e^{-x}-2}{x^2}\)
\(=\lim\limits_{x \to 0} \frac{e^{2x}+1-2e^x}{x^2e^x}\)
\(=\lim\limits_{x \to 0} (\frac{e^x-1}{x})^2\times e^{-x}\)
\(=\lim\limits_{x \to 0} (\frac{e^x-1}{x})^2\times \lim\limits_{x \to 0}e^{-x}\)
= 1 × e0
= 1.