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c)octave-3.6.1.exe:1> x=[2 9 16]

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x =

2 9 16

octave-3.6.1.exe:2> y=[2^(1/2)*17^(1/2) 3*17^(1/2) 4*17^(1/2)]

y =

5.8310 12.3693 16.4924

octave-3.6.1.exe:3> c=polyfit(x,y,2)

c =

-0.024646 1.205153 3.519229

octave-3.6.1.exe:4> P2=polyout(c)

P2 = -0.024646*s^2 + 1.2052*s^1 + 3.5192

octave-3.6.1.exe:5> P=polyval(c,x)

P =

5.8310 12.3693 16.4924

octave-3.6.1.exe:6> Ps=polyval(c,12)

Ps = 14.432

octave-3.6.1.exe:7> erP=(14.2828-14.4321)*100/14.2828

erP = -1.0453

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d) erL=erP=-1,0453%

e) octave-3.6.1.exe:1> x=2:0.1:16;

octave-3.6.1.exe:2> N2=-0.0246*x.^2+1.2046*x. 1+3.5202;

octave-3.6.1.exe:3> L2=-0.0246*x.^2+1.2052*x.^1+3.5192;

octave-3.6.1.exe:4> P2=-0.0246*x.^2+1.2052*x.^1+3.5192;

octave-3.6.1.exe:5> f=sqrt(17)*x.^(1/2);

octave-3.6.1.exe:6> plot(x,f,"o1",x,L2,"o2",x,N2,"*4",x,P2,"+2"),grid("on")

Problema 2

octave-3.2.4.exe:1> x=[1 2 3 4 5]

x =

1 2 3 4 5

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octave-3.2.4.exe:2> y=[-17*2 17*2 17 17/10 17*10]

y =

-34.0000 34.0000 17.0000 1.7000 170.0000

octave-3.2.4.exe:3> yi=spline(x,y)

yi =

{

x =

1

2

3

4

5

P =

10.4833 -73.9500 131.4667 -34.0000

10.4833 -42.5000 15.0167 34.0000

34.2833 -11.0500 -38.5333 17.0000

34.2833 91.8000 42.2167 1.7000

n = 4

k = 4

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d = 1

}

octave-3.2.4.exe:4> valinterp1=ppval(yi,(2.6))

valinterp1 = 29.974

octave-3.2.4.exe:5> valinterp2=ppval(yi,(4.2))

valinterp2 = 14.090

octave-3.2.4.exe:6> x=[1 2 3 4]

x =

1 2 3 4

octave-3.2.4.exe:7> y=[-17*2 17*2 17 17/10]

y =

-34.0000 34.0000 17.0000 1.7000

octave-3.2.4.exe:8> p=polyfit(x,y,3)

p =

14.450 -129.200 354.450 -273.700

octave-3.2.4.exe:9> pp=polyout(p)

pp = 14.45*s^3 - 129.2*s^2 + 354.45*s^1 - 273.7

octave-3.2.4.exe:10> x=1:0.1:4;

octave-3.2.4.exe:11> y=14.45*x.^3-129.2*x.^2+354.45*x. 1-273.7;

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octave-3.2.4.exe:12> yi=spline(x,y,x)

yi =

Columns 1 through 7:

-34.00000 -20.90405 -9.43840 0.48365 8.94880 16.04375 21.85520

Columns 8 through 14:

26.46985 29.97440 32.45555 34.00000 34.69445 34.62560 33.88015

Columns 15 through 21:

32.54480 30.70625 28.45120 25.86635 23.03840 20.05405 17.00000

Columns 22 through 28:

13.96295 11.02960 8.28665 5.82080 3.71875 2.06720 0.95285

Columns 29 through 31:

0.46240 0.68255 1.70000

octave-3.2.4.exe:13> plot(x,yi),grid("on")

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Problema 3

octave-3.6.1.exe:1> j=5*((17*((-5/sqrt(3)+6)^2+1))/(1+log(-5/sqrt(3)+6))+(17*((5/sqrt(3)+6)^2+1))/(1+log(5/sqrt(3)+6)))

j = 2560.2

octave-3.6.1.exe:2> er1=(17*150.8745-j)/(17*150.8745)*100

er1 = 0.18297

octave-3.6.1.exe:3> x=[1 6 11]

x =

1 6 11

octave-3.6.1.exe:4> function y=f(x)

> y=17*(x^2+1)/(1+log(x))

> endfunction

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octave-3.6.1.exe:5> format long

octave-3.6.1.exe:6> i=quad("f",1,11)

i = 2564.86654798786

octave-3.6.1.exe:7> er2=(17*150.8745-i)/(17*150.8745)*100

er2 = -1.87096911061579e-006

octave-3.6.1.exe:8>y=[17*(1^2+1)/(1+log(2)) 17*(6^2+1)/(1+log(6)) 17*(11^2+1)/(1+log(11))]

y =

20.0809477110878 225.3059430560197 610.3778467227263

octave-3.6.1.exe:9> k=5/3*(20.0809+4*225.3059+610.3778)

k = 2552.80383333333

octave-3.6.1.exe:10> er3=(17*150.8745-k)/(17*150.8745)*100

er3 = 0.470303880013509

Problema 4

4.1)

octave-3.6.1.exe:1> x=0:2:24;

y=[17*65 17*67 17*79 17*97 17*120 17*143 17*164 17*180 17*189 17*187 17*172 17*140

17*89]

y =

Columns 1 through 11:

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1105 1139 1343 1649 2040 2431 2788 3060 3213 3179 2924

Columns 12 and 13:

2380 1513

octave-3.6.1.exe:2> c=polyfit(x,y,3)

c =

-1.0185 26.3969 -29.7348 1103.4588

octave-3.6.1.exe:3> P=polyout(c)

P = -1.0185*s^3 + 26.397*s^2 - 29.735*s^1 + 1103.5

octave-3.6.1.exe:4> F=polyval(c,x)

F =

Columns 1 through 8:

1103.5 1141.4 1341.7 1655.3 2033.5 2427.3 2787.8 3066.1

Columns 9 through 13:

4.2)

octave-3.6.1.exe:6> trapz(x,y)

ans = 54910

octave-3.6.1.exe:7> sum(-1.0185*x.^3 + 26.397*x.^2 -29.735*x.^1 + 1103.5)

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ans = 2.8767e+004

3213.4 3180.7 2919.2 2380.0 1514.2

4.3)

octave-3.6.1.exe:8 > grid("on"),plot(x,y,"-*3;graficul zilnic de sarcina(tabel);"), hold("on")

octave-3.6.1.exe:9> plot(x,-1.0185*x.^3 + 26.397*x.^2 -29.735*x.^1 + 1103.5,"-o1;functia P=P(t)(punctul

1) ;")