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for $$x_i \ge 0$$, determine: $\underset{r\to 0}{\mathop{\lim }}\,{{\left( \frac{{x_1}^r+{x_2}^r+\cdots +{x_n}^r}{n} \right)}^{\frac1r}}=\ldots$

Note by Idham Muqoddas
3 years, 5 months ago

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The Generalized mean Wikipedia article proves that the limit is simply the geometric mean of the $$x_i$$'s.

Click on the first "show" link in the Definition section. · 3 years, 5 months ago