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\wip + + Siano $\int_a^b f(x) \, dx$ e $\int_a^b g(x) \, dx$ due integrali + impropri semplici in $b$. + + \begin{proposition} + Se $o \leq f \leq g$ in un intorno di $b$, allora: + + \begin{enumerate}[(i)] + \item Se $\int_a^b f(x) \, dx = +\infty$, allora + $\int_a^b g(x) \, dx = +\infty$. + + \item Se $\int_a^b g(x) \, dx < +\infty$, allora + $\int_a^b f(x) \, dx < +\infty$. + \end{enumerate} + \end{proposition} + + \begin{proposition} [confronto asintotico debole] + Se $f$, $g \geq 0$ in un intorno di $b$ e $f(x) = O(g(x))$ + per $x \to b^-$, allora: + + \begin{enumerate}[(i)] + \item Se $\int_a^b f(x) \, dx = +\infty$, allora + $\int_a^b g(x) \, dx = +\infty$. + + \item Se $\int_a^b g(x) \, dx < +\infty$, allora + $\int_a^b f(x) \, dx < +\infty$. + \end{enumerate} + \end{proposition} + + \begin{proposition} [confronto asintotico forte] + Se $f$, $g \geq 0$ in un intorno di $b$ e esiste $0 < m < +\infty$ tale + che $f(x) \sim m g(x)$ per $x \to b^-$, allora i due integrali + impropri hanno lo stesso comportamento. + \end{proposition} +\end{document} diff --git a/Geometria 1/Scheda riassuntiva/main.pdf b/Geometria 1/Scheda riassuntiva/main.pdf index 20f906d81b6dbbc83327488589d2d0079b6d4d5a..8a11d475d2cf5bb24e80f4c679538dab60d7b8ba 100644 GIT binary patch delta 21379 zcmV(rK<>YsyAtlY60qwJ0x~$4@Sy=If9*ZllHZxa$!7n&Il*J~fBD1LpZ^|qGIvE*7-4XuMz3d^_yf0A2~X@#GeEpm?y1WCiro39vGyXv^w)W3K+?BNG? zzuuot`}$YMRk{(JWZ@cCwcc=kWOuC~=~`if~baEcAD ze*eJ(aGSmV0pK>SV{v^PlCQVo*p4*v`w0Pj~z6>98Rv zTG&hrK3kNReQ^hxe?8~wP8IM5AYewMoyrsl;bAcikV|+QRoF~0Ia5r(?n7i%W|*D> z5$J0nN91n~dLvH(`YnOPMEt%bSxdtIhjCc&EVuj?I4n#ifyfe&-_~qQ0cJAJ%?K(v z11id|#bw88fX!Im1&xxS)-+OJwLcDsQIHl!MgkiY3&of`e>bsEf936(Jt`!yHCdzQ zMamULEXT>UO=fNSjAr6KD9B%xyQlqjUmIep{qxJ=!P&L^{^*Ul)4?mz%5yI4sz4IN zM%w!9*ZU6P-GCu@sJue{H{vVeRe-dN9OGZy7N1bLfuoie5?^YrNRe?k6P1H~E4_XD ziU3My-0Cs1f0JNDFf#|HDHcW>(&`RO$6#|;tNqR&$Nq5IKkawrwhE?AeRdwpM}L^^ zi@peW53ojkxkqa46?;gk=z2)3_K<-1gNLMwm>Ftge-(aL8>SXVo@j#QaQf`(lxj<>L(!*aLh31 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