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Sarcini pentru problemele de Programare Liniara
Sarcina 1
Metoda grafică de rezolvare a Problemei de Programare Liniară (PPL).
Variante pentru Sarcina 1
| Nr var | Problema de programare liniara | Nr var | Problema de programare liniara |
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|  max f (x) = 3X1 + 2X2
X1 + 2X2 ≥ 10
2X1 - X2 ≤ 18
X1 + 3X2 ≤ 13
X1, X2 ≥ 0
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|  max f (x) = 3X1 + 2X2
 X1 + 2X2 ≤ 12
2X1 - X2 ≥ 7
X1 + 3X2 ≥ 14
X1, X2 ≥ 0
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| max f (x) = 3X1 + 2X2 X1 + 2X2 ≤ 11 2X1 - X2 ≥ 5 X1 + 3X2 ≥ 14 X1 , X2 ≥ 0 | ||
|      min f (x) = 3X1 + 2X2
 X1 + 2X2 ≥10
2X1 - X2 ≥ 10
X1 + 3X2 ≤ 13
X1, X2 ≥ 0
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| max f (x) = 3X1 + 2X2 X1 + 2X2 ≤ 11 2X1 - X2 ≥ 5 X1 + 3X2 ≥ 14 X1 , X2 ≥ 0 |  , 
 
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| max (10х1 + 20х2) х1 + х2 £ 150 2 х1 + 0.5 х2 £ 240 х1 + 3.5 х2 £ 350 х2³ 60, х1 ³ 0 | 
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| max f (x) = 3х1+ х2 х1 + х2 £ 5 0.5х1 + х2 ³ 3 х1 - х2 ³ 1 | 
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| max f (x) = 3х1+ х2 2х1 + 3х2 ³ 12 -х1 + х2 £ 2 2х1 - х2 £ 2 х1 ³ 0, х2 ³ 0 | 
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| min f (x) = 3X1 + 2X2 X1 + 2X2 ≤ 11 2X1 - X2 ≥ 5 X1 + 3X2 ≥ 14 X1, X2 ≥ 0 | L = 5x1 - 2x3  min - 5x1 - x2 + 2x3 ≤ 2 - x 1+x3 + x4 ≤ 5 - 3x1 + 5x4 ≤ 7
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| max f (x) = 3х1+ 5х2 х1 + х2 £ 5 3х1 + 2 х2 £ 8 х1 ³ 0, х2 ³ 0 | 
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| min f (x) = 3X1 + 2X2 X1 + 2X2 ≥12 2X1 - X2 ≥ 12 X1 + 3X2 ≤ 14 X1, X2 ≥ 0 | 
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max f (x) = 4х1+ 3х2
 х1 + 2х2 £ 10
х1 + 2х2 ³ 2
2х1 + х2 £ 10
х1 ³ 0, х2 ³ 0
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Sarcina 2
Limita şirului numeric. Erorile de calcul.
Variante pentru Sarcina 2
Demonstraţi ca numărul a este limita şirului numeric cu preciziile
· 𝜀=0.01
· 𝜀=0.001
| 1. |  =0
| 24. | 
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| 2. |  =11
| 25. |  =1/5
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| 3. | lim (2n-1)/(2n+1)=1 n®¥ | 26. | lim ( )=1/3
n®¥
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| 4. | lim (3n2+1)/(5n2-1)=3/5 n®¥ | 27. | lim ( )=1/2
n®¥
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| 5. | lim (3n-5)/(9n+4)=1/3 n®¥ | 28. | lim ( )=1
n®¥
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| 6. | lim (n2-2)/(2n2-9)=1/2 n®¥ | 29. | lim ( )=1
n®¥
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| 7. | lim (3n+1)/ 3n =1 n®¥ | 30. | lim (2n-1)/(2n+1)=1 n®¥ |
| 8. | lim (1/2n)=0 n®¥ | 31. | lim n!/((n+1)!-n!)=0 n®¥ |
| 9. | lim (an/n!)=0, pentru a>0 n®¥ | 32. | lim (n2)/(n3+2009)=0 n®¥ |
| 10. | lim ( )=0
n®¥
| 33. | lim (n+1)/n=1 n®¥ |
| 11. | lim ( )=1
n®¥
| 34. | lim ((n+2)!+(n+1)!)/(n+3)!)=0 n®¥ |
| 12. | 
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| 36. |  
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| 16. |   =0
| 39. |  =6 
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| 17. |  = 
| 40. |  =3
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| 18. |  =0
| 41. |  = 
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| 19. |  =2
| 42. |  = 
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| 20. |  =e2
| 43. |  =20
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| 21. |  =1
| 44. |  =0
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| 22. |  =0
| 45. |  = 
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| 23. |  =2
| 46. |  = 
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Sarcina 3
Calcularea aproximativă a valorii funcţiei utilizînd diferenţiala. Erorile de calcul.
Variante pentru Sarcina 3
1. Calculaţi valoarea aprovimativă a funcţiei de o singură variabilă in punctul x=a
2. Calculaţi valoarea aprovimativă a funcţiei de 2 variabile
In punctul x=a,y=b
3. Evaluaţi erorile
| Var | Functia de o singura variabila | Functia de 2 variabile |
| y=sin(x), x=310, | z=x2+  , x=1,y=4,01
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| y=cos(x), x=610, | z= ex +  , x=1,y=8,01
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| y=ex, x=1,05, | z=x2+ , x=1,y=4,01
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| y=2x4-x3+3, x=1,05 | z=  + , x=1,05,y=4,01
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| y=3x3+x-1, x=1,05 | z=sin(x+y), x=1,05,y=0,01 | |
| y=ln(1+e10x), x=0,05 | z=ln(x+y), x=1,05,y=0,01 | |
| y=arctg(e3x), x=0,05 | z=  , x=1,05,y=4,01
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y=  , x=0,15
| z=  , x=1,05,y=4,01
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| y=lg(x), x=10,21 | z=  (x+y2), x=1,05,y=0,001
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y=  , x=33
| z= x2+y+ln(x+y), x=1,05,y=0,01 | |
| y= lg(10*sin(x)), x=910 | z= x+y2+ln(x2+y), x=0,05,y=1,001 | |
| y= x10-3x6+x2+2, x=0,05 | z=x2+2xy+y2, x=0,05,y=0,001 | |
| y=24ex-24x3-18x-2, x=0,01 | z=x2y/(x2+y2), x=1,05,y=1,01 | |
| y=6sinx+x3, x=0,05 | z=e(x+y)/(xy), x=0,01,y=0,01 | |
| y=2cosx+x2, x=0,01 | z=tg(xy2), x=0,05,y=0,01 | |
| y=x80-x10+x20, x=0,005 | z=xy/(x+y), x=0,05,y=2,01 | |
y=  , x=0,05
| z=xy, x=1,05,y=1,01 | |
y=1/  , x=0,05
| z=x2y3, x=1,05,y=1,01 | |
| y=2cos + , x=0,01
| z=xy/  , x=1,05,y=4,01
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y=  , x=0,01
| z=4x2-3xy, x=1,05,y=4,01 | |
| y= ln(1+x), x=0,05 | z=2xy+3x2-y2, x=1,05,y=4,01 | |
| y= sinx+ex, x=0,01 | z=exsiny, x=-3.01,y=4,02 | |
| y= ex+x3, x=0,001 | z=(1+xy)2, x=0,05,y=2,02 | |
| y= /(x2+1), x=0,01
| z=ln(1-xy+y2), x=1.03,y=2,06 | |
| y=3x3+x- ln(x), x=1,05 | z=e(x+y), x=1,02,y=3,06 | |
y=  , x=0,001
| z=(x2+y2)/(x+y), x=1.01,y=1.01 | |
| y=3x3+x- sin(x), x=0,001 | z=x2y/(x+y), x=0,05,y=0,01 | |
| y= + sin(x), x=0,01
| z=(x2+y2)ex, x=0,05,y=0,01 | |
| y=tg(x)+ ex, x=0,01 | z=(x2+y2)ey, x=0,05,y=0,01 | |
| y= x2008-x2009+x2010, x=1,001 | f(x,y,z)=arctg(1,05) +  +
+  .
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y=  , x=0,05
| Stiind ca  ,calculati
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y=1/  , x=0,05
| Stiind ca f(x,y,z)=x2+lnx+ ez,, calculati f(x,y,z)= 1,012+ln(0,07)+e1,03, | |
| y=2sin + x3, x=0,03
| f(x,y)= sinx+y2+ln(x2+y), x=0,01,y=1,003 | |
y=  , x=0,04
| Stiind ca f(x,y,z)=sin2x+ey+arcsinz, calculati f(x,y,z)= sin2(0,05)+2 e1,01+arcsin(1,03), | |
| y= cos(1+x), x=0,05 | f(x,y)= x4y/(x2+tg2y), x=1,05,y=1,02 | |
| y= tgx+ex, x=0,02 | f(x,y,z)= e(x+y)/(xy)+ 2sin  , x=0,01,y=0,01, z=1,01
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| y= tg30+sin2280 | f(x,y)=  , x=0,02,y=0,04
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y=  /(x2+1), x=0,01
| f(x,y,z)= xy/(x2+y2)+  , x=0,05,y=2,01,z=1,03
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| y=3x2+cosx- sin(x), x=0,05 | f(x,y)=  , x=1,02,y=1,04
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y=  , x=0,05
| f(x,y,z)= x2+y3-z5, x=1,02,y=1,03, z=2,04 | |
| y=x2- sin2(x), x=0,03 | f(x,y)= cos2x+lny+e(x+y), x=1,05,y=1,01 | |
y=  + arcsin(x), x=0,02
| f(x,y)=(x+y2)/ln(x2+y), x=0,05,y=1,001 | |
| y=tg(x)+ ex, x=0,01 | f(x,y,z)= sin(x2+2xy+y2)+zxy, x=0,02,y=0,01, z=0,06 | |
| y= sin(x)+cos(x)+ex, x=1,001 | f(x,y)= cos(x2y)/(x2+y2), x=1,05,y=1,01 | |
| y=arctg(1,05) | f(x,y,z)= e(x+y)/(z+y)+exyz, x=0,01,y=0,01, 1,01 | |
| y=1/(e0,05+tg30+sin50+ln1.05) | f(x,y)= tg(xsin2y), x=0,05,y=0,01 |
Sarcina 4
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