Limitele unor siruri integrale
Posted: Tue Jun 24, 2008 8:41 pm
Fie \( f:[0.\infty)\rightarrow\mathbb{R} \) o functie continua marginita, cu f(0)=0.
a) Aratati ca \( \lim_{n\to\infty}\int_0^1{f(nx^n)dx}=0 \).
b) Calculati \( \lim_{n\to\infty}\int_0^1{\sqrt{1+n^2x^{2n}}dx}. \)
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a) Aratati ca \( \lim_{n\to\infty}\int_0^1{f(nx^n)dx}=0 \).
b) Calculati \( \lim_{n\to\infty}\int_0^1{\sqrt{1+n^2x^{2n}}dx}. \)
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