Integrala - Admitere SNSB

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Diana Putan
Euclid
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Joined: Wed Sep 26, 2007 11:37 pm
Location: Bucuresti

Integrala - Admitere SNSB

Post by Diana Putan »

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
"Dispretuiesc proportiile, masurile, tempo-ul lumii obisnuite. Refuz sa traiesc in lumea obisnuita ca o femeie obisnuita.(...) Nu ma voi conforma lumii. Ma conformez doar mie insami."
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m3adi3c
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Joined: Thu Jan 08, 2009 4:24 pm
Location: Buzau

Post by m3adi3c »

http://pro-didactica.ro/forum/index.php ... 8&ID=20433 :)
Adi M.
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