Esercizi svolti per l'esame Metodi matematici

Esercizio prova+1✗)

-2×fa e=Dominio{ È}ERI(e) Eco✗ -10C☐ = , I+2 a-1a- (f) 1) v32] trano=☐ -- ,,monotonia +1✗ ) e)f) -2 (×l' ( -21e ✗× += -•. ape 22)(, × -✗ -2 ☒) ☒f ( -21- -1× -= . .)2ft -212(×+1✗ 1-2✗ ¢>-3 °e= .• 22 a)( X -✗ -2 f)EIR / EIRl'f' 1=0(✗ <o✗ ✗i ]ft ]in-- -1no- ,+a-1 a-0 fù ] [2in + ✗,Asintoti verticali È+1✗ lei è-2lim × =Laee ✗+ a.=== r-- .a+→✗ +1✗ è-2×lim A.=3e 0e== y .a✗ → " ^i://t.ir .^ \,

Esercizio variabilifunzionidi prova Duea/

)flx ) )( (-1 a- 5,0✗ ×y =, 13=(7/0)-3tay✗ )( 5,1E- -0✗O✗ = -1=0-1=0 =L ✗✗ ✗ - -+2×-3=0✗ ++•÷;;,Mhhyyy+ +ti -+ +2. =3 ✗✗ - ✗3-✗ = 2✗ yso ' •a3-O +2 =1- I 2×-3=0/o 1) )( (d1 -1✗ × x✗- = DX)a 2ft-3ay✗ -3+ +2gy ✗, )(2×-111×+2×-3) (1 -1✗= x-) +2×-312(2ft ✗y, 2×2+4 21 +2×+3Gx ✗✗✗ + ×= y -- - 23))2ft ( ay+✗y -,Of 21 -6×+411×+2×+3✗= ( 23))2pAOX ay✗ +y -, )Of (O1 -1✗ ✗= =.dy ) dy2ft +2×-3✗y, ( )0 A)l')( €1-1 ¥-1x✗= = -• ,dy +2×-3) ✗2ft ))(fay, )(1 2-1✗✗= • - 23)) (2ft ay✗y + -, )df 2×111 ×= -) 2( 3)2ftOy tay✗y -, { 2-6×+4 +2×+3=0✗ ✗ y2×(1-11)=0 >C ben=L lontaniOVX punti✗ = dalte triangolo> delall'V interno triangolo• Ba D ciche vadacapitanon mai Oyad annullarsiteha punticercaresensonondove laannullisi

Triangolostudio perimetrosul del

) [( ]fa (AB f 5,7✗× C-×y =, ,>, 0) +le¥ -°/ 75 3+56E3- 2-6×+3of ✗1= o>=( × 2( 3)2ft, XOx -,2-6×+3>-0 0=24✗ TÈTG rg3- 2=3✗ +✗è sottoTg no3-a --) )fac ( [=p ]AC ( C- 0,15× ✗y y, ,f )d ( 5 Y, 1-o ^dy )df () -40( 1-5 zoy == , (OY ) 2×+2122115 y,)fpgc (BC XB✗× Y Y YB- -=, ✗ XB YC YBc- --7 +2×-7=0✗ ✗y=75- -2g7✗ =f ) ][( ay 0,1ye7- y,) 2×2-13×+21/ (7-2×-1) 2×2-13×+21f (( -2g ay7 7y = - = =, Fa7- ay -3ay 2+) 2×2-13×+21(f §§ fa-247 Y =,, (4×-13)2×2-13×+21d IO1=dy aya2 -13×+21 ÷13 -YZ IO4O +- ¥ a+a-}maxt-maxsfl-N.lk}minfminsfk fin) ,a) tof( /=p 20 Max5 -= = -, 2=pf( 42/B) 217 max== =, 24)) =p /ff §205,1 min== =4(3+56,0) ) 6+256+36+6f 3+612+6(D) 12+556=p = = == No ☒31+8-31 min=2015

Gennaio13 la2)

1 K 0O D=I 1K OKTII1 -1ti1 KO 1 K I ] )la / ( K211 1- -1 KK t =- === a -a - --1 -1-1 K2I K 1 += =--K2 K 2= -- )2) (( K Kid-2K 1-K= = - }{lato KE -1,2¢ }{ =DK A--1,2 dee✗ .{ }K calcolo creato-1,2 10 e-¥0c- KI )b)( /a 1 0KO= I O1K Kia11- -1→ 100 O1 K +10Ih == 1kt ,IKTII bK A- ind-1 ✗= =K bincomp2 1- ✗= = .{ }# -1,2casok→ K0o 01 ( K21) )1I (O KK KK -114- k+ += === -- - -una-1IKTI ti 41 O I ¥ ( )1)1) (( KostkaK2 hnK -11-K O +1 = == - =-- } ha1 K hKts -1 + I= ---11 1 -111 1221 01 )) (( 2+2×+1 -1✗ ✗ )Http / -1K( )ktplkk¥1 ) k¥1( -1- , , -2K¥-211k¥k¥1 )2) ) ()( ( ( kK k- a)( KZ y-1K ,- /K -2 KK -2 -e)(k= -1caso E-0-110 0111- Ey✗{ × ✗ .e- =-tytt e✗ +✗ y =- - -1 O te--11 -{ {✗ .= e-✗ =✗ e-e- + e+ ✗ ✗ == -- -- oy =() )✗ §e-y ER= e-z

13 Gennaio 1- B2015)

aflx -1✗= 2+5×+4✗Dominio }HER '/ -1(f) cotal× e☐ 2+5×+4✗ {{ 2-1=0✗ una⇐✗2+5×+4>0 tu -1>< ×✗✗ -I-51=3/-4 2- 1-✗ III ✗±= 2+5×+4,& \ -4 ea -1 +- ⑤⑤e- (f) ( tal[=] + U +1no☐ - -, ,monotonia 2×1×75×+4f) ) (2×+5)1)(l' x21= =- -.2 (-1 2+5×+472 ✗ ✗2+5×+4✗ )+8×-12×32×3+10×2 -2×+5×2-51= =.)f( 2+5×+412(2 ✗×5×2+10×+5201 .)2ft ( 2+5×+47✗2+2×+11=0 +11220(( EIRb- b- ✗✗✗ talpt ]+ no- ,a+a-Asintoti verticali2- 1-✗lim -415 + A.+ aa ✗ v= == = .4-→ +2+5×+4✗ - ✗ ☐2 -1✗lim 1^ =L A. 0✗= = .Ia→ 2+5×+4✗ ✗Grafico i a

Gennaio 20152A131)

)fa x2log- 2+4×+3✗ }{ ERI(f) a +0CE)✗ ✗ °☐ = /2+4×+3✗{ {a > o✗ > o×2+4×+3 >UX -1-3o <> ✗✗ ④⑦ ④tilt 2+16-12=4ba tac ✗D= -- t{ {{ 2+4×+3++ +-3 ✗-10-3-0 tra-41=2=✗ 2 -1 (f) ] v30-3C [ tal]Uno -1,0☐ = - ,,monotonia )2×(+74×+3) (2×+4))( ( x22+4×+3f' X ✗= -.2 2+4×+312(✗ ✗☒ (2×3+4×2)3+8×2+62+4×+3✗ × -.2 2+4×+312(✗✗ )(f' )212×+34×2+62+4×+3 zo× =zo✗ ×. )( 2+4×+32+4×+3122 ✗ ✗(✗ ✗)(f' )212×+3 20× = )( 2+4×+3✗ ✗ NN+ +-{ { Xx + ++2×+3=0 -= -=✗ - }'2 +-_ i -o > o×>✗ UN' +2+4×+3>0 ++-3✗ -1< >×u✗ -3 -10