Tabella dei limiti notevoli
I limiti notevoli servono a risolvere le forme indeterminate. Ecco le tabelle dei limiti notevoli
£$ \displaystyle \begin{array}{|cccc|c|c|c|} \hline{\text{Esponenziali e logaritmi}}\\ \hline{\lim\limits_{x\to \pm\infty}\left(1+\frac{a}{x}\right)^{x}=e^{a}}\\ \hline {\lim\limits_{x\to 0}(1+ax)^{\frac{1}{x}}=e^{a}} \\ \hline {\lim\limits_{x\to 0}\frac{\ln(1+x)}{x}=1} \\ \hline {\lim\limits_{x\to 0}\frac{e^x - 1}{x}=1} \\ \hline {\lim\limits_{x\to 0}\frac{a^x-1}{x}=\ln(a)} \\ \hline \end{array}$£
£$ \displaystyle \begin{array}{|cccc|c|c|c|}\hline{\text{Funzioni goniometriche}}\\ \hline{\lim\limits_{x\to 0}\frac{sen\,x}{x}=1}\\ \hline {\lim\limits_{x\to 0}\frac{sen\,ax}{bx}=\frac{a}{b}} \\ \hline {\lim\limits_{x\to 0}\frac{1-cos\,x}{x}=0} \\ \hline {\lim\limits_{x\to 0}\frac{1-cos\,x}{x^2}=\frac{1}{2}} \\ \hline {\lim\limits_{x\to 0}\frac{tgx}{x}=1} \\ \hline \end{array}$£