• Author / Uploaded
• Gean Antonny Gamarra Damian

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UNIVERSIDAD SANTO TORIBIO DE MOGROVEJO

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NOMBRES: CAMPOS LLONTOP ENRIQUE

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DOCENTE: BETTY RIMARACHI

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CURSO: METODOS NUMERICOS

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CICLO: 2016-II

EJERCICIO 1 PARTE I

clc clear x=-3:0.01:3; y1=x.^2; y2=x+2; plot(x,y1,'g',x,y2,'k','linewidth',2) grid on

9 8 7 6 5 4 3 2 1 0 -1 -3

-2

-1

0

1

>> p0=1.5,tolerancia=10^(-6), N=50 p0 = 1.5000 tolerancia = 1.0000e-006 N = 50 >> [p1]= newton('fn2','dfn2',p0,tolerancia,N) 1 2.125000000000 2 2.004807692308 3 2.000007680020 4 2.000000000020 5 2.000000000000

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p1 =

2

PARTE II >> p0=0,tolerancia=10^(-6), N=50 p0 = 0 tolerancia = 1.0000e-006 N= 50 >> [p1]= newton('fn2','dfn2',p0,tolerancia,N) 1 -2.000000000000 2 -1.200000000000 3 -1.011764705882 4 -1.000045777066 5 -1.000000000698 6 -1.000000000000 p1 =

-1

PARTE III >> p0=10,tolerancia=10^(-6), N=50 p0 = 10 tolerancia = 1.0000e-006 N= 50 >> [p1]= newton('fn2','dfn2',p0,tolerancia,N) 1 5.368421052632 2 3.165291607397 3 2.254738454603 4 2.018490413795

5 2.000112577399 6 2.000000004224 7 2.000000000000 p1 = 2

PARTE IV >> p0=-30,tolerancia=10^(-6), N=50 p0 = -30 tolerancia = 1.0000e-006 N= 50 >> [p1]= newton('fn2','dfn2',p0,tolerancia,N) 1 -14.786885245902 2 -7.217035116248 3 -3.504298934398 4 -1.783097522884 5 -1.134300380120 6 -1.005518138624 7 -1.000010112749 8 -1.000000000034 9 -1.000000000000 p1 = -1 PARTE V >> p0=-100,tolerancia=10^(-6), N=50 p0 = -100 tolerancia = 1.0000e-006

N= 50 >> [p1]= newton('fn2','dfn2',p0,tolerancia,N) 1 -49.761194029851 2 -24.652980088422 3 -12.121216354813 4 -5.899743801769 5 -2.875660187861 6 -1.521098236276 7 -1.067177182924 8 -1.001439777823 9 -1.000000690324 10 -1.000000000000 p1 = -1.0000

EJERCICIO 2 clc

clear x=-3:0.01:3; y1=x; y2=2.^(-x); plot(x,y1,'g',x,y2,'k','linewidth',2) grid on

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PARTE I >> p0=1,tolerancia=10^(-8), N=40 p0 = 1 tolerancia = 1.0000e-008 N= 40 >> [p1]= newton('fn3','dfn3',p0,tolerancia,N) 1 0.628687207584 2 0.641169034643 3 0.641185744475 4 0.641185744505

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p1 = 0.6412 PARTE II >> p0=0,tolerancia=10^(-8), N=40 p0 = 0 tolerancia = 1.0000e-008 N= 40 >> [p1]= newton('fn3','dfn3',p0,tolerancia,N) 1 0.590616109150 2 0.640909617724 3 0.641185736374 4 0.641185744505 p1 = 0.6412 PARTE III >> p0=10,tolerancia=10^(-6), N=50 p0 = 10 tolerancia = 1.0000e-006 N= 50 >> [p1]= newton('fn3','dfn3',p0,tolerancia,N) 1 0.007740338488 2 0.591904230224 3 0.640923588441 4 0.641185737176

5 0.641185744505 p1 = 0.6412 PARTE IV >> p0=100,tolerancia=10^(-6), N=100 p0 = 100 tolerancia = 1.0000e-006 N= 100 >> [p1]= newton('fn3','dfn3',p0,tolerancia,N) 1 0.000000000000 2 0.590616109150 3 0.640909617724 4 0.641185736374 5 0.641185744505 p1 = 0.6412

PARTE V >> p0=-100,tolerancia=10^(-6), N=100 p0 = -100 tolerancia = 1.0000e-006 N= 100 >> [p1]= newton('fn3','dfn3',p0,tolerancia,N) 1 -98.557304959111 2 -97.114609918222

3 -95.671914877333 4 -94.229219836444 5 -92.786524795555 6 -91.343829754666 7 -89.901134713777 8 -88.458439672888 9 -87.015744631999 10 -85.573049591110 11 -84.130354550221 12 -82.687659509332 13 -81.244964468443 14 -79.802269427555 15 -78.359574386666 16 -76.916879345777 17 -75.474184304888 18 -74.031489263999 19 -72.588794223110 20 -71.146099182221 21 -69.703404141332 22 -68.260709100443 23 -66.818014059554 24 -65.375319018665 25 -63.932623977776 26 -62.489928936887 27 -61.047233895998 28 -59.604538855109 29 -58.161843814220 30 -56.719148773331 31 -55.276453732442 32 -53.833758691553

33 -52.391063650664 34 -50.948368609775 35 -49.505673568886 36 -48.062978527997 37 -46.620283487108 38 -45.177588446218 39 -43.734893405328 40 -42.292198364435 41 -40.849503323535 42 -39.406808282617 43 -37.964113241653 44 -36.521418200568 45 -35.078723159166 46 -33.636028116939 47 -32.193333072571 48 -30.750638022648 49 -29.307942958355 50 -27.865247856978 51 -26.422552660179 52 -24.979857218623 53 -23.537161151510 54 -22.094463492037 55 -20.651761797875 56 -19.209049934868 57 -17.766312600675 58 -16.323511927875 59 -14.880555112723 60 -13.437217398261 61 -11.992962461826 62 -10.546534550806

63 -9.095066327502 64 -7.632236890731 65 -6.144857635497 66 -4.608207550077 67 -2.988724915620 68 -1.308252622248 69 0.084951730837 70 0.603765762454 71 0.641035037232 72 0.641185742083 73 0.641185744505 p1 = 0.6412

EJERCICIO 3 clc clear x=-3:0.01:3; y1=x.^(3); y2=x+4; plot(x,y1,'g',x,y2,'k','linewidth',2) grid on

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PARTE I >> p0=1,tolerancia=10^(-8), N=50 p0 = 1 tolerancia = 1.0000e-008 N= 50 >> [p1]= newton('fn4','dfn4',p0,tolerancia,N) 1 3.000000000000 2 2.230769230769 3 1.881118881119 4 1.800478486494

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5 1.796332590707 6 1.796321903330 7 1.796321903259 p1 = 1.7963

PARTE II >> p0=2,tolerancia=10^(-8), N=50 p0 = 2 tolerancia = 1.0000e-008 N= 50 >> [p1]= newton('fn4','dfn4',p0,tolerancia,N) 1 1.818181818182 2 1.796613025529 3 1.796321955862 4 1.796321903259 5 1.796321903259 p1 = 1.7963

PARTE III >> p0=0.5,tolerancia=10^(-8), N=50 p0 = 0.5000 tolerancia = 1.0000e-008 N= 50

>> [p1]= newton('fn4','dfn4',p0,tolerancia,N) 1 -17.000000000000 2 -11.341801385681 3 -7.570452974129 4 -5.053093591455 5 -3.360379055941 6 -2.186726617245 7 -1.267325326886 8 -0.018577859559 9 -4.004133098035 10 -2.641171550562 11 -1.648411969258 12 -0.693300167767 13 7.541955916146 14 5.081187983710 15 3.484083057814 16 2.501246773562 17 1.986457359315 18 1.815565838327 19 1.796548023217 20 1.796321934996 21 1.796321903259 22 1.796321903259 p1 =

1.7963

PARTE IV >> p0=0.1,tolerancia=10^(-8), N=100 p0 = 0.1000 tolerancia =

1.0000e-008 N= 100 >> [p1]= newton('fn4','dfn4',p0,tolerancia,N) 1 -4.125773195876 2 -2.725558722778 3 -1.714485370549 4 -0.777568042065 5 3.759658323459 6 2.663579913710 7 2.060462960752 8 1.831498363504 9 1.797067258182 10 1.796322247938 11 1.796321903260 12 1.796321903259 p1 =

1.7963

EJERCICIO 4 clc clear x=-3:0.01:3; y1=cos(x); plot(x,y1,'g','linewidth',2) grid on

1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -10

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PARTE I

0

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>> p0=3,tolerancia=10^(-6), N=50 p0 = 3 tolerancia = 1.0000e-006 N= 50 >> [p1]= newton('fn5','dfn5',p0,tolerancia,N) 1 -4.015252551435 2 -4.852657566279 3 -4.711461741169 4 -4.712388980650 5 -4.712388980385 p1 = -4.7124

PARTE II >> p0=5,tolerancia=10^(-6), N=50 p0 = 5

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tolerancia = 1.0000e-006 N= 50 >> [p1]= newton('fn5','dfn5',p0,tolerancia,N) 1 4.704187084467 2 4.712389164306 3 4.712388980385 p1 = 4.7124