1. Din 100 mere, 10 sunt stricate. Care este probabilitatea ca scotind 5 mere la intiplare, sa avem cel putin un mar stricat?2. La o loterie sunt 96 bilete, dintre care 8 cistigatoare. O persoana cumpara 12 bilete. Sa se determine probabilitatea ca:a) Exact un bilet sa fie castigator.b) Sa nu uasa niciun bilet castigator.3. Trei furnizori de aparate casnice aprovizioneaza un depozit in proportie de 45%, 35% si respective 20%. Primul furnizor are 3% aparete defectate, al doilea 4%, iar al treilea 5%. Sa se determine procentul aparatelor defecte din deposit.4. Din urna U(4a, 3n), se efectueaza trei extrageri, fara repunerea bilei extrase inapoi in urna. Scrieti variabila aleatoare care descrie numarul bilelor albe ce se pot obtine.1. O urna contine 7 bile albe, 5 bile rosii si 3 bile albastre. Aflati probabilitatea ca extragind simultan 3 bile:a) Toate bilele sa fie de culoari diferite;b) Cel putin doua bile sa fie de culoare rosie;2. Un tren soseste la ora fixate cu probabilitatea p=0, 9. Sa se determine probabilitatea ca intr-o saptamina trenul sa intirzie de doua ori.Se considera doua urne avind compozitiile. Se extrage o bila din fiecare urna. Sa se determine probabilitatea de a obtine o bila alba.Un fotbalist transforma lovitura de la 11 metri cu probabilitatea.Care este probabilitatea ca el sa inscrie in trei din patru lovituri de pedeapsa?1. Fie ecuatia 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 Care este probabilitatea ca aruncind doua zaruri, numerele obtinute sa fie radacinele ecuatiei date?2. Fie o urna care contine 4 bile albe si 6 bile negre. Se extrage o bila din urna, iar in locul ei se introduce alta bila de cealalta culoare. Se extrage din nou o bila. Sa se determine probabilitatea ca cele doua bile sa fie de culori diferite.3. Se considera o urna care contine 4 bile albe si 2 bile negre. Se extrag simultan doua bile din urna. Fie X variabila aleatoare care asociaza, la fiecare extragere, numarul de bile extrase. Sa se determine legea deprobabilitate, valoarea medie si dispersia variabilei aleatoare X.1.Aflati aria subgraficului functiei a) f:[0;1] f(x)=x2 -2x +2011;b) f:[-2;4] f(x)=2x2 -7x +3.2.Calculati aria figurii, marginite de liniile: y=0,5x2 , y=0, x=33.Calculati aria fidurii, limitata de liniile y=2sinx , y=-sinx , 0=0 pentru care este adevrat inegalitatea: < +bdx x016 ) 3 (Pag 158. Determinati primitivele functiilor:a) f : 222 3) ( , ) , 0 (x x xx f R + .9. Determinati primitivele functiilor:a)b) f : 13 3) ( , ) , 1 (2+ + xx xx f R.10. Determinati primitivele functiilor:a) f : x x x f R ln ) ( , ) , 0 (2+ ;b) f : xe x x f R R+ ) 1 ( ) ( ,;c) f : ) 5 2 3 ( ) ( ,2 x x e x f R Rx d) f : x arctg x f R R ) ( ,;e) f : x n x x f R R21 ) ( , ;f) f : x x x f R R cos ) ( ,2 ;11. Determinati primitivele urmatarelor functii2ln) ( , ) , 0 ( : )x xx f R f a xexx f R R f b1) ( , : )+ x arctg x x f R f c ) ( , ) , 0 ( : )12. Determinati primitivele functiilor:a)x e x f R R fxsin ) ( , :2 b)x e x f R R fx2 cos ) ( , :3 c)1 ) ( , :2+ x x f R R fd)24 ) ( , : x x f R R f 13. Determinati primitivele functiilor:a)xxx f R fln) ( , ) , 0 ( : ;b); 1 ) ( , :2+ x x x f R R fc); 9 ) ( , ) 3 , 3 ( :2x x x f R f d); cos sin ) ( , :3x x x f R R f e)2) 1 ( ) ( , ) , 0 ( : + x x f R f14. Determinati primitivele functiilor:a)x arctg x x f R R f2) ( , : ;b)xxx f R fln) ( , ) , 0 ( : ;c); 1 ) ( , : *2+ + x x x f R R fd)2arcsin) ( , ) 1 , 0 ( : *xxx f R f ;e)11) ( , :+ xxeex f R R f;P 158 4.9 Integrarea prin substituii1. Determinai x > 0, astfel nct xedt tt20 ) 3 ln 2 (1 2. Calculati:a) ++10219 2dxxx; b) dxx x+1041 44;3.Calculai :b) +elx xdx) 1 (ln2; 12 pd) dxeexx+101;f) dxxx210211

,_

+; 4.Calculati:a) ; cos sin2203xdx x;b); cos sin3202xdx xc) dxeexx+101;a. De calculat:a) 315ln xdx xb)

,_

+dxxx2021111P 1651. () = 3 2 Calculai aria suprafeei plane cuprins ntre graficul funciei f, axa Ox i dreptele x = 0 i x = 1.P 1664 () = 3 3 Determinai aria suprafeei plane cuprins ntre graficul funciei f, axa Ox i dreptele de ecuaii x = +1 i x = 1.12. Seconsider funcia f : R R, f(x) = -x2 + 4x 3. Determinai a (1, 3) cu proprietatea c dreapta x a mpate suprafaa plan cuprins ntre graficul funciei f i axa Ox n dou regiuni de arii egale13. Determinai aria cuprins ntre graficile funciilor f, g: R R, f(x) = x2 +4x, g(x) = x +414. Se consider funciile f, g: R R, f(x) = x2 5x +3 ig(x) 3+ 3x x2.a) Rezolvai inecuaia f(x) g(x).b) Calculai aria suprafeei plane cuprins ntre graficile celor dou funcii.15. Considerm funcia f : R {1} R, 1) (2+xx xx f. Calculaiariamulimii plane mrginit de graficul funciei f, axa Oy, asimptota oblic i dreapta de ecuaie x = -116. Se consider funcia f : R R, f(x) = x2 3. Calculai aria suprafeei plane limitat de graficul funciei f, tangenta la grafic n punctul de abscis 2 i dreptele de ecuaii x = 0 i x = 2.19. Determinai numrulreal a, astfel nct volumul corpului obinut prin rotaia n jurul axei Ox a graficului funciei f : [0, 1] R, f(x) = 3x + 2 .21. Calculai volumul corpului de rotaia deteminat de funcia f : 1]1

21, 0R, f(x) = arcsin x.22. Calculai volumul corpului de rotaia deteminat de funcia f : 1]1

21, 0R, f(x) = 2x + 3.I.S se calculeze aria subgraficului urmtoarelor funcii:1. [ ]2: 0,1 , ( ) 3 2 1 f R fx x x + +2. [ ]) 1 (1) ( , 2 , 1 :+ x xx f R f3. [ ]xe x x f R f ) ( , 1 , 0 :4. [ ]: 0, 5 , ( ) 4 f R fx x x +5. [ ]) 3 )( 2 )( 1 (1) ( , 2 , 0 :+ + + x x xx f R f6. arccos , [0,1]:[0, 2] , ( )1, (1, 2]x xf R fxx x ' II. S se calculeze aria mulimii , fgA n cazurile:1. [ ] 1 , 0 , 1 ) ( , 2 3 7 ) (2 2 + + + x x x x g x x x f2. [ ] 3 , 1 ,11) ( , ) (22+ xxx g x x f 3. [ ] 1 , 0 ,21) ( ,) 2 )( 1 (5 4) ( ++ ++ xxx gx xxx f4. [ ] 2 , 1 , ) ( , ) ( x e x g e x x fx x5. [ ] 1 , 0 , ) ( , ) (3 x x x g e x fxIII. 1. S se determine aria cuprins ntre dreapta de ecuatie y = 4x + 1 i parabola y = x2+4.2.S se determine aria cuprins ntre parabolele 24 y x i 25 y x .3.S se determine aria cuprins ntre parabolele 3 42 + x x y