Limiti
Inviato: 14 ago 2007, 13:38
Qualcuno potrebbe spiegarmi come si arriva a questi risultati?
$ $ \lim_{p\rightarrow 0} \left( \frac{{a_1}^p+{a_2}^p+\cdots +{a_n}^p}{n}\right)^{\frac{1}{p}}=\sqrt[n]{{a_1}{a_2}\cdots {a_n}} $
$ $ \lim_{p\rightarrow +\infty} \left( \frac{{a_1}^p+{a_2}^p+\cdots +{a_n}^p}{n}\right)^{\frac{1}{p}}=\max\{{a_1},{a_2},\cdots {a_n}\} $
$ $ \lim_{p\rightarrow -\infty} \left( \frac{{a_1}^p+{a_2}^p+\cdots +{a_n}^p}{n}\right)^{\frac{1}{p}}=\min\{{a_1},{a_2},\cdots {a_n}\} $
$ $ \lim_{p\rightarrow 0} \left( \frac{{a_1}^p+{a_2}^p+\cdots +{a_n}^p}{n}\right)^{\frac{1}{p}}=\sqrt[n]{{a_1}{a_2}\cdots {a_n}} $
$ $ \lim_{p\rightarrow +\infty} \left( \frac{{a_1}^p+{a_2}^p+\cdots +{a_n}^p}{n}\right)^{\frac{1}{p}}=\max\{{a_1},{a_2},\cdots {a_n}\} $
$ $ \lim_{p\rightarrow -\infty} \left( \frac{{a_1}^p+{a_2}^p+\cdots +{a_n}^p}{n}\right)^{\frac{1}{p}}=\min\{{a_1},{a_2},\cdots {a_n}\} $