Integrala - Admitere SNSB
Posted: Wed Mar 12, 2008 11:07 pm
Fie \( f:[0, 1] \to (0,\infty) \) o functie continua. Pentru \( \alpha>0 \), definim
\( F(\alpha) =\int^{1}_{0}{f(t)^{\alpha}dt}. \)
(a) Aratati ca \( F \) e derivabila pe (0,1).
(b) Calculati \( \lim_{\alpha\to0}{F(\alpha)^{\frac{1}{\alpha}}} \).
(c) Calculati \( \lim_{\alpha\to\infty}{F(\alpha)^{\frac{1}{\alpha}}} \).
Admitere SNSB, 2006
\( F(\alpha) =\int^{1}_{0}{f(t)^{\alpha}dt}. \)
(a) Aratati ca \( F \) e derivabila pe (0,1).
(b) Calculati \( \lim_{\alpha\to0}{F(\alpha)^{\frac{1}{\alpha}}} \).
(c) Calculati \( \lim_{\alpha\to\infty}{F(\alpha)^{\frac{1}{\alpha}}} \).
Admitere SNSB, 2006
