Inegalitate diferential-integrala

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Cezar Lupu
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Inegalitate diferential-integrala

Post by Cezar Lupu »

Daca \( f:[0, \infty) \to\mathbb{R} \) este o functie derivabila cu derivata continua atunci \( | f(x) | \leq | f(0) | +\int_0^x | f(t)+ f^\prime (t)|dt \), oricare ar fi \( x\geq 0 \).
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
aleph
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Post by aleph »

Notăm g = f + f'. Rezultă f(x) = exp(-x) [ f(0) + int_[0,x] g ]
şi inegalitatea e imediată.
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