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\OT1/cmr/m/it/10 dove il sec-ondo mem-bro e' un in-sieme che con-tiene fun-zion
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[][] \OML/cmm/m/it/10 '\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OM
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[] \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/
cmm/m/it/10 dx \OMS/cmsy/m/n/10 ^^@ [][] \OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OM
L/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx \OMS/cmsy/m/n/10 ^^T \OT1/
cmr/m/n/10 0  \OMS/cmsy/m/n/10 ,  [][] \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/
cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx \OMS/cmsy/m/n/10 ^^T [][] \O
ML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m
/it/10 dx
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[][] \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OM
L/cmm/m/it/10 dx \OT1/cmr/m/n/10 + [][] \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML
/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx [][] f\OT1/cmr/m/n/10 (\OML
/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx \OMS/cmsy/m/n/10 ^^U \OT1/c
mr/m/n/10 0 + [][] \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cm
r/m/n/10 ) \OML/cmm/m/it/10 dx \OT1/cmr/m/n/10 + 0 = [][] \OML/cmm/m/it/10 f\OT
1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx
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[16]
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[17] [18]
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[19] [20]
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[21]
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\OML/cmm/m/it/10 f \OT1/cmr/m/n/10 : (\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 ) []
[]\OMS/cmsy/m/n/10 ! \U/msb/m/n/10 R\OML/cmm/m/it/10 ;  []  \OMS/cmsy/m/n/10 ) 
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[24]
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\OML/cmm/m/it/10 X[];  Y[]  \OMS/cmsy/m/n/10 )  \OML/cmm/m/it/10 Y[];  [] X \OT
1/cmr/m/n/10 = [] \OML/cmm/m/it/10 Y
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\OML/cmm/m/it/10 X \OMS/cmsy/m/n/10 \ \OML/cmm/m/it/10 ^^Y \OT1/cmr/m/n/10 = []

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[26]
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[]\OT1/cmr/m/n/10 Esiste in-fatti un cer-chio di cen-tro $\OML/cmm/m/it/10 I\OT
1/cmr/m/n/10 (\OML/cmm/m/it/10 O; r\OT1/cmr/m/n/10 )$, di rag-gio $\OML/cmm/m/i
t/10 r > [] []$
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\OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 " > \OT1/cmr/m/n/10 0 \OMS/cmsy/m/n/10 9\OML
/cmm/m/it/10 ^^N > \OT1/cmr/m/n/10 0 :  \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 P; [
] \OT1/cmr/m/n/10 :  \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 P\OMS/cmsy/m/n/10 j \OM
L/cmm/m/it/10 < ^^N  \OMS/cmsy/m/n/10 )  \OML/cmm/m/it/10 S\OT1/cmr/m/n/10 (\OM
L/cmm/m/it/10 f; P\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 s\OT1
/cmr/m/n/10 (\OML/cmm/m/it/10 f; P\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 < "  \OT1/
cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^C\OT1/cmr/m/n/10 )
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[27]
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[28]
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[29]
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[]\OT1/cmr/m/n/10 Trasliamo $\OML/cmm/m/it/10 f; g$ \OT1/cmr/m/n/10 in modo da 
avere $\OML/cmm/m/it/10 G[]; G[] \OMS/cmsy/m/n/10 ^^U \OT1/cmr/m/n/10 0$, per p
oi ap-pli-care il thm [[][]2.2[][],pg.[][]26[][]]: 
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[] \OML/cmm/m/it/10 T\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 f[]; g[]\OT1/cmr/m/n/10 
) = [][] \OML/cmm/m/it/10 g[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10
 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x
\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx \OT1/cmr/m/n/10 = [][] \OML/cmm/m/it/10 g
\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/
cmm/m/it/10 m \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/
m/it/10 x\OT1/cmr/m/n/10 ) + \OML/cmm/m/it/10 m dx \OT1/cmr/m/n/10 = [][] \OML/
cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n
/10 ^^@ \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) 
\OML/cmm/m/it/10 dx
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\OT1/cmr/m/n/10 Diremo che $\OML/cmm/m/it/10 f$ \OT1/cmr/m/n/10 e' in-te-gra-bi
le in senso gen-er-al-iz-zato in $[\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 ]$ se $
\OMS/cmsy/m/n/10 9[]  [][] [][] \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/i
t/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx$
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[30]
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\OT1/cmr/m/n/10 Diremo che $\OML/cmm/m/it/10 f$ \OT1/cmr/m/n/10 e' in-te-gra-bi
le in senso gen-er-al-iz-zato in $[\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 ]$ se $
\OMS/cmsy/m/n/10 9[]  [][] [][] \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/i
t/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx$
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[31]
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[32]
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[33]
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\OT1/cmr/m/n/10 Diremo che $\OML/cmm/m/it/10 f$ \OT1/cmr/m/n/10 e' in-te-gra-bi
le in senso gen-er-al-iz-zato in $[\OML/cmm/m/it/10 a; \OT1/cmr/m/n/10 +\OMS/cm
sy/m/n/10 1\OT1/cmr/m/n/10 [$ se $\OMS/cmsy/m/n/10 9[]  [][] [][] \OML/cmm/m/it
/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx$
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\OT1/cmr/m/n/10 Diremo che $\OML/cmm/m/it/10 f$ \OT1/cmr/m/n/10 e' in-te-gra-bi
le in senso gen-er-al-iz-zato in $] \OMS/cmsy/m/n/10 ^^@ 1\OML/cmm/m/it/10 ; b\
OT1/cmr/m/n/10 ]$ se $\OMS/cmsy/m/n/10 9[]  [][] [][] \OML/cmm/m/it/10 f\OT1/cm
r/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx$
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[34]
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[35]
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[36]
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[] \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) [] 
\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) [] (\OML
/cmm/m/it/10 a; b\OT1/cmr/m/n/10 )  \OMS/cmsy/m/n/10 ,  8\OML/cmm/m/it/10 x \OM
S/cmsy/m/n/10 2 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 ) \OMS/cm
sy/m/n/10 8\OML/cmm/m/it/10 " > \OT1/cmr/m/n/10 0 \OMS/cmsy/m/n/10 9 [] 2 \U/ms
b/m/n/10 N \OT1/cmr/m/n/10 :  \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 f[]\OT1/cmr/m/
n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10
 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 j \OML/c
mm/m/it/10 < " \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 n > v
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[37]
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[] []  \OMS/cmsy/m/n/10 ,  8\OML/cmm/m/it/10 " > \OT1/cmr/m/n/10 0 \OMS/cmsy/m/
n/10 9\OML/cmm/m/it/10 v \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 v\OT1/cmr/m/n/10 (\
OML/cmm/m/it/10 "\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 2 \U/msb/m/n/10 N \OT1/cmr/
m/n/10 :  \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/
10 x\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 
(\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 j \OML/cmm/m/it/10 < " \OM
S/cmsy/m/n/10 8\OML/cmm/m/it/10 n; m > v \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 x \
OMS/cmsy/m/n/10 2 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 )
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[38]
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\OT1/cmr/m/n/10 questo vuol dire che, fis-sato $\OML/cmm/m/it/10 n > v[]$\OT1/c
mr/m/n/10 , $[]$ e' un mag-gio-rante di $[][]$,
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[39]
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[] \OML/cmm/m/it/10 L[] \OT1/cmr/m/n/10 = 0  \OMS/cmsy/m/n/10 ,  8\OML/cmm/m/it
/10 " > \OT1/cmr/m/n/10 0 \OMS/cmsy/m/n/10 9\OML/cmm/m/it/10 v \OT1/cmr/m/n/10 
= \OML/cmm/m/it/10 v\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 "\OT1/cmr/m/n/10 ) \OMS/c
msy/m/n/10 2 \U/msb/m/n/10 N \OT1/cmr/m/n/10 :  \OMS/cmsy/m/n/10 j\OML/cmm/m/it
/10 L[] \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/10 0\OMS/cmsy/m/n/10 j \OT1/cmr/m/n/1
0 = \OML/cmm/m/it/10 L[] \OT1/cmr/m/n/10 = [] \OMS/cmsy/m/n/10 j\OML/cmm/m/it/1
0 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ 
\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OMS/cmsy
/m/n/10 j \OML/cmm/m/it/10 < " \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 n > v
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[]\OT1/cmr/bx/n/10 Example 4.5. []\OT1/cmr/m/n/10 Ri-con-ducen-doci all'esempio
 visto in [[][]4[][],pg.[][]37[][]], ap-plichi-amo quest'ultimo
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[40]
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[41] <fig/fn.png, id=812, 206.7725pt x 100.375pt>
File: fig/fn.png Graphic file (type png)
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[42]
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[43 <./fig/fn.png (PNG copy)>]
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\OML/cmm/m/it/10 f[] [] f [] \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 a; b\OT1/cmr/m/n
/10 ]  \OMS/cmsy/m/n/10 )  9\OML/cmm/m/it/10 v[] \OT1/cmr/m/n/10 = \OML/cmm/m/i
t/10 v[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 "\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 2
 \U/msb/m/n/10 N \OT1/cmr/m/n/10 :  \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 f[] \OMS
/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/
m/n/10 )\OMS/cmsy/m/n/10 j \OML/cmm/m/it/10 < [] \OMS/cmsy/m/n/10 8\OML/cmm/m/i
t/10 n > v[] \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 2 \OT1/cmr/m
/n/10 [\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 ]  (1)
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[44]
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[] \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) [] 
\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) [] (\OML
/cmm/m/it/10 a; b\OT1/cmr/m/n/10 )  \OMS/cmsy/m/n/10 ,  9 []\OML/cmm/m/it/10 ; 
 [] \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 2 \U/msb/m/n/10 N \OM
L/cmm/m/it/10 L[] \OMS/cmsy/m/n/10 ^^U \OT1/cmr/m/n/10 0  :  \OMS/cmsy/m/n/10 j
\OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OMS/cm
sy/m/n/10 j ^^T \OML/cmm/m/it/10 L[] \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 n \OMS/
cmsy/m/n/10 2 \U/msb/m/n/10 N \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 x \OMS/cmsy/m/
n/10 2 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 )
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\OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 " > \OT1/cmr/m/n/10 0  \OMS/cmsy/m/n/10 9\OM
L/cmm/m/it/10 v \OMS/cmsy/m/n/10 2 \U/msb/m/n/10 N \OT1/cmr/m/n/10 :  \OMS/cmsy
/m/n/10 j\OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10
 ) + \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) +
 [] + \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\
OMS/cmsy/m/n/10 j \OML/cmm/m/it/10 < " \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 n > v
  \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 p \OMS/cmsy/m/n/10 2 \U/msb/m/n/10 N  \OMS
/cmsy/m/n/10 8\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 2 \OT1/cmr/m/n/10 (\OML/cmm/m
/it/10 a; b\OT1/cmr/m/n/10 )
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[46]
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\OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 " > \OT1/cmr/m/n/10 0 \OMS/cmsy/m/n/10 9\OML
/cmm/m/it/10 v \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 v\OT1/cmr/m/n/10 (\OML/cmm/m/
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10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) + \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (
\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) + [] + \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 
(\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 j \OML/cmm/m/it/10 < " \OM
S/cmsy/m/n/10 8\OML/cmm/m/it/10 n > v \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 p \OMS
/cmsy/m/n/10 2 \U/msb/m/n/10 N \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 x \OMS/cmsy/m
/n/10 2 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 )
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\OT1/cmr/m/n/10 Per il cri-te-rio di con-ver-genza delle se-rie nu-meriche di C
auchy, dire che $[][] []$
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/cmm/m/it/10 v \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 v\OT1/cmr/m/n/10 (\OML/cmm/m/
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jj \OML/cmm/m/it/10 < " \OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 n > v \OMS/cmsy/m/n/
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\OML/cmm/m/it/10 T[] \OT1/cmr/m/n/10 = [][] \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10
 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx \OT1/cmr/m/n/10 + [] 
+ [][] \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )
 \OML/cmm/m/it/10 dx \OT1/cmr/m/n/10 = [][] \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10
 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) + [] + \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/1
0 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 dx \OT1/cmr/m/n/10 = []
[] \OML/cmm/m/it/10 s[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OM
L/cmm/m/it/10 dx
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\OT1/cmr/m/n/10 0 \OML/cmm/m/it/10 < r \OMS/cmsy/m/n/10 ^^T \OT1/cmr/m/n/10 +\O
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\OMS/cmsy/m/n/10 9 [] []\OML/cmm/m/it/10 ; [] \OT1/cmr/m/n/10 :  \OMS/cmsy/m/n/
10 j\OML/cmm/m/it/10 a[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 ^^
@ \OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 )[]\OMS/cmsy/m/n/10 j ^^T \OML/cmm/m/it/1
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mm/m/it/10 x[] \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 ^^N; x[] \OT1/cmr/m/n/10 +
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\OT1/cmr/m/n/10 poiche' $\OML/cmm/m/it/10 h \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10
 H$\OT1/cmr/m/n/10 , si ha che la se-rie nu-mer-ica (a ter-mini non neg-a-tivi)
 $[][] \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 a[]\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10
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\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) = \OML/c
mm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 ) + [](\OML/cm
m/m/it/10 x \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 ) + [](\OM
L/cmm/m/it/10 x \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 )[] + 
[] + [](\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 x[]\OT1/cmr/m/
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\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 ) + [](\
OML/cmm/m/it/10 x[] \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 ) 
+ [] + [](\OML/cmm/m/it/10 x[] \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 x[]\OT1/cm
r/m/n/10 )[] + [] = \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]\OT1
/cmr/m/n/10 ) + 0 + 0 + [] = \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/1
0 x[]\OT1/cmr/m/n/10 )
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[]\OT1/cmr/bx/n/10 Definition 8.10. []\OT1/cmr/m/n/10 Se $\OML/cmm/m/it/10 X$ \
OT1/cmr/m/n/10 non e' lim-i-tato, pos-si-amo dare quest'ulteriore definizione: 

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\OMS/cmsy/m/n/10 9\OML/cmm/m/it/10 " > \OT1/cmr/m/n/10 0 : []\OMS/cmsy/m/n/10 8
\OML/cmm/m/it/10 ^^N > \OT1/cmr/m/n/10 0[][]\OMS/cmsy/m/n/10 9\OML/cmm/m/it/10 
x; y \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 X \OT1/cmr/m/n/10 :  \OML/cmm/m/it/10 
d\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x; y\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 < ^^N
[][][]d[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x
\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ;  f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 y\OT1/c
mr/m/n/10 )) \OMS/cmsy/m/n/10 ^^U \OML/cmm/m/it/10 "[][][][]\OT1/cmr/m/n/10 (1)

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\OT1/cmr/m/n/10 Data $\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1
/cmr/m/n/10 ) : \OML/cmm/m/it/10 X [][]\OMS/cmsy/m/n/10 ! \U/msb/m/n/10 R[]\OML
/cmm/m/it/10 ;   X[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 S; d\OT1/cmr/m/n/10 )\OML
/cmm/m/it/10 ; [] \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 X$\OT1/cmr/m/n/10 , con $
\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) = (\OML/
cmm/m/it/10 f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OML/cmm/m/i
t/10 ; f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 
; [] ; f[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )) :
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\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x; y\OT1/cmr/m/n/10 ) = \OM
L/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]; y[]\OT1/cmr/m/n/10 ) + []
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[][] \OT1/cmr/m/n/10 = [] [] [][] (\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 ^^@ \OML
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\OML/cmm/m/it/10 S \OT1/cmr/m/n/10 = []
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\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ;  \O
T1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; [] ; 
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 $\OML/cmm/m/it/10 H[]$ \OT1/cmr/m/n/10 e' con-tinua, perche' prodotto e dif-fe
renza di fun-zioni con-tinue. Poiche'
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 \OT1/cmr/m/n/10 Uti-lizzi-amo la for-mula di Tay-lor ar-restata alle derivate 
sec-onde (vedi [[][]9.6[][],pg.[][]100[][]]):
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 \OT1/cmr/m/it/10 In sostanza, per trovare i punti di es-tremo as-so-luto, bast
a cer-care in $\OML/cmm/m/it/10 X[][]X[][]X[]$\OT1/cmr/m/it/10 . 
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[]\OT1/cmr/bx/n/10 Example 9.8. []$\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/
m/it/10 x; y\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/10 y[] \OMS/cmsy/m/n/10 ^^@ \OML/
cmm/m/it/10 x[] \OT1/cmr/m/n/10 : \OML/cmm/m/it/10 X [][]\OMS/cmsy/m/n/10 ! \U/
msb/m/n/10 R$\OT1/cmr/m/n/10 , con $\OML/cmm/m/it/10 X \OT1/cmr/m/n/10 = \OML/c
mm/m/it/10 C\OT1/cmr/m/n/10 ((0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0)\OML/cmm/m/
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