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== Limiti notevoli ==
=== Limiti notevoli di funzioni goniometriche ===
: <math>\lim_{x\to0}{\frac{\sin{x}}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} 1</math>
: <math>\lim_{x\to0}{\frac{\sin{\epsilon(x)}}{\epsilon(x)}} \stackrel{\left[\frac{0}{0}\right]}{=} 1</math>
: <math>\lim_{x\to0}{\frac{\sin{\emph{a}x}}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} \emph{a}</math>
: <math>\lim_{x\to0}{\frac{\tan{x}}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} 1</math>
: <math>\lim_{x\to0}{\frac{1-\cos{x}}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} 0</math>
: <math>\lim_{x\to0}{\frac{1-\cos{x}}{x^{2}}} \stackrel{\left[\frac{0}{0}\right]}{=} \frac{1}{2}</math>
=== Limiti notevoli di funzioni esponenziali ===
: <math>\lim_{x\to\infty}{\left(1+\frac{1}{x}\right)^{x}} \stackrel{\left[\infty^{0}\right]}{=} e</math>
: <math>\lim_{x\to\infty}{\left(1+\frac{1}{\epsilon(x)}\right)^{\epsilon(x)}} \stackrel{\left[\infty^{0}\right]}{=} e</math>
: <math>\lim_{x\to\infty}{\left(1+\frac{\emph{a}}{x}\right)^{x}} \stackrel{\left[\infty^{0}\right]}{=} e^{\emph{a}}</math>
: <math>\lim_{x\to\infty}{\left(1-\frac{1}{x}\right)^{x}} \stackrel{\left[\infty^{0}\right]}{=} \frac{1}{e}</math>
: <math>\lim_{x\to0}{\left(1 + x\right)^{\frac{1}{x}}} \stackrel{\left[1^{\infty}\right]}{=} e</math>
: <math>\lim_{x\to0}{\left(1 + \epsilon(x)\right)^{\frac{1}{\epsilon(x)}}} \stackrel{\left[1^{\infty}\right]}{=} e</math>
: <math>\lim_{x\to0}{\left(1 - x\right)^{\frac{1}{x}}} \stackrel{\left[1^{\infty}\right]}{=} \frac{1}{e}</math>
: <math>\lim_{x\to\stackrel{x_0}{\infty}}lim{f(x)^{g(x)}} = \lim_{x\to\stackrel{x_0}{\infty}}lim{e^{g(x)\cdot\ln{f(x)}}}</math>
=== Limiti notevoli di funzioni contenenti logaritmi o esponenziali ===
<math>\lim_{x\to0}{\frac{\ln{(1 + x)}}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} 1</math>
<math>\lim_{x\to0}{\frac{\log_{\emph{a}}{(1 + x)}}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} \log_{a}{e} = \frac{1}{\ln{a}}</math>
<math>\lim_{x\to0}{\frac{\ln{(1 + \epsilon(x))}}{\epsilon(x)}} \stackrel{\left[\frac{0}{0}\right]}{=} 1</math>
<math>\lim_{x\to0}{\frac{e^{x} - 1}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} 1</math>
<math>\lim_{x\to0}{\frac{\emph{a}^{x} - 1}{x}} \stackrel{\left[\frac{0}{0}\right]}{=} \ln{\emph{a}}</math>
<math>\lim_{x\to0}{\frac{e^{\epsilon(x)} - 1}{\epsilon(x)}} \stackrel{\left[\frac{0}{0}\right]}{=} 1</math>
<math>\lim_{x\to0}{\frac{\emph{a}^{\epsilon(x)} - 1}{\epsilon(x)}} \stackrel{\left[\frac{0}{0}\right]}{=} \ln{\emph{a}}</math>
[[Categoria:Matematica per le superiori|Limiti]]
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