Prove d'esame Matematica

07.2119Tema del '2+5×+8)f

( ✗x1 =. ti✗ 1) a)(faD D=-1ti -1 +1=0 ≠✗> ✗ - ,, i-2+5×+8)ff 2+5×+8✗≥ o >✗ 0ti≥ D:0✗ ≥No : _ _1✗ the+ ✗D t>A -1o< -8)Alo , 2-5×+8ffx)fa ) ✗Pari no→ = = I+✗- x2)) 2-5×+8ffx(f- SX✗Dispari -8=× no=→ - -=- ti✗ ✗ 1- - -# )2+5×+8 ¥(✗ +✗ ✗ itun so= = -)☒ ( ¥✗ ✗ io +→ 1 +- 2+5×+8✗un too=so ti✗ ✗+→ 1+-5++82+5×+8Un ✗ + so= = }l'l'✗ - - Uerticau✗+ o→ ✗ =, AS-- .l'2+5×+8 1-S'Un +8 =×✗ -ao= - = --✗ -1 -O→ +✗ , #☒2+5×+8 )¥(lui it✗ 11 m= =m → ='✗ )± ( ¥io +→ ×✗ 1 +# è2+5×+8Un +5×+8 +8✗ UX 4✗ U→ q- - =q ==✗ =,Io +1✗ ✗→ ✗ i++✗ iObliquo 5-4✗ 0Asintoto 44 yY+lf ✗0✗= I✗= = y= == =, ,) (+2+5×+8)/(2×+5)' ( )f 2+2×-32×2+2 2+1✗ #S# -8t +✗ ✗-= ✗=× - - =2 221)( (1)( 1)+ +✗✗ ✗+' 2+2×-3)f- ( /> ✗o 16× N ±✗0> 22: = -,,( 1) 2+✗ 1 3✗ 3✗ 1V >✗<= ✗>= - -z, }{ IRthe -D -: ff-)(M -3 -1, -7)( 1 /m ), .À(2×+2)2-2) 3)( ( 1) ( ')" /f ✗ + tzx✗ + ✗× m= - =")( ✗ i+ )(2×+2)/+72×+1 )( 2×3+2×2 UXZTUX -6×-6+-= =")( +1✗+2×+2*+41×+2Hot È È # 8×+8# 2¥ +6×+6 0= =- >- - "( )")( +1+ ✗i✗ ) i(8×+8 '8 +1N ✗ >: 0 Flessi✗ l>o NO, -{ }"( ) V. IRD iC- /:+1 ✗ -✗ U .•.• Ei4=+1-4 ' ))(' Risolverezx cosìSintcosiUn possa+ ( se+ sisonon✗2 . '(✗ tanx )0 tanx→ sinx✗+✗ + ?( )? 2tanx) x2( tanxSinxnxStrix ✗-✗✗ -0per ~→ ,, .( )2 23 2☒ ✗+ COSXUn COSX + ✗✗✗2x + 2+ ==. )(2 3✗ x2O it→ +✗ ✗☒+✗ + ✗ ( ]?)(f-

4 Teorema Lagrange

× ✗=3 × -1,0--. I✗ - ][D= 1 1,0≠ IN✗ Continua )f' ((1) 2-)( 2×2( ) 22U× ✗× ✗I= 2x +4 2×+5- - ti ✗- - # #✗× -- -==21)( 21)21) ((× ✗- x - -)1) '( f-DerivabileD= ≠ IN0 1 1,0≠x ✗- (b)f- )fla 1(c)f' U - 3= - = =b- a 1)C2 362S2C 2+ s3 (Zctl +zc- == _-,)( c' S?c- 6C +3 +2C3C O, =---? C2 2C2C 2 I o4C = =O -- -- 8 Fe±2 it=C. =a 2 Fa1-| t 2T dtDXdi S✗SU ==×✗ --.. t' S✗= -5)t' t.lt/ t'( dt +5✗+ = 2ft 10ft/ ') "t' sta dt2) dt dt(t' t' dts ++2+ ' 3(≥ 5)ts tot )(2 toS ×2 c > -x+ + a- ++3s g 3'{)f( ≥= ✗✗ i+2×S -. g)( '' §' Za+✗ I<aat + ×✗ - --✗ -1= )')( ffiUn §§Continua 1: la+ a• =+- --_✗ ,→ - §?§ 1laaQ1 + =-- - -±9 177=a 6{( ) 1f' =× ^≥×33 ( 2) 2✗ + )( +1-3ZX + a ✗ 1< )Deriuabiutà f'(( )atflui +2. I✗: = -✗ → 1-- 2- ¥ §Un •+ + ='-,✗ -→ 2a ='La diderivabile stesso valorefunzione lo acontinuae e pernon in,quanto 'e : ) /( ±9 177 6continua per =•- derivabile 2aper =-

6.09.21Deltema 2+2×-3)f

( ✗1 =×. 2×+4 ( (-2,1-0)) 2)D=D: 21×+22×+4+-0 -1-0 io -- ,f- ( ) 2+2×-3 1≥ ±-2≥ UO o =✗ ✗N× ✗ = 1-3: V ✗ ≥≤✗e i2 ✗ 3= -a ???- -02×+4 > ✗ > -2D:)(A 0-3 , )( 1B 0 +t --, 2+2×-3✗Un a= -2×1-4so✗ → - 2+2×-3Un ✗ oo+=✗ 2×+4so+→ 2+2×-3 S -✗ - 32- U -un - si= - +== ±2×+4 -U '2- 0✗ tu As verticale2.✗-→ - = - .2+2×-3 St2+-4+-3✗Un so- === -" 2×+4 O'✗ -2 -U' tu-→ - )¥2+2×-3 ¥(☒ l'un ✗ ↓- 12- m→ -= =È' )¥/=D 2×2✗ ux→ 2. ++2+2×-3 2×2+41×-6 2¥ 4UX 6 ✗Un ✗ -{ -= -✗ =_± • )( 4×+4✗ → 2 ✗ +2×+4 2. 0u 0 12{6 OBUQUO Y 4AS= 2= o ✗- =→.± a ) ?( '(2×+2)/2×+4 -2×2--4×+63))f' ( +8×+4&tim