Soluzione Esercizio 2

 

            \begin{align} \lim_{x \to 0} \frac{e^x-e^{-x}-2x} {x-\operatorname{sen}(x)} &=&\\ &=\xrightarrow{l'H \hat{o} pital} \lim_{x \to 0} \frac{e^x-(-e^{-x})-2}{1-\operatorname{cos}(x)} =\\ &=\xrightarrow{l'H \hat{o} pital} \lim_{x \to 0} \frac{e^x-e^{-x}}{\operatorname{sen}(x)} =\\ &=\xrightarrow{l'H \hat{o} pital} \lim_{x \to 0} \frac{e^x-(-e^{-x})}{\operatorname{cos}(x)} =\\ &=\frac{e^0+e^{-0}}{\operatorname{cos}(0)} =\frac{1+1}{1} = 2\end{align}