gràfica de un aecuaciòn y localizaciòn de raìces

GRÀFICA Y LOCLIZACIÒN DE RAÌCES DE UNA ECAUCIÒN

ECUACIÒN: y= f(x)=2cos(x) ^(x)-(2x^2)-2/3+�

1ª Opciòn

x y=2cos(x) ^(x)-(3x^2)-2/3+� Signo f(x)-1.5 -7.0520621032 --1 -2.2181826138 -

-0.5 0.9450291168 +0 2.3333333333 +

0.5 1.9872197278 +1 0.1322197735 +

1.5 -2.793503193 -2 -6.1099042408 -

2.5 -8.8364599371 -3 -9.5611147367 -

Tabla nª 01

2ª Opciòn

x y1 =2cos(x) ^(x)+� Y2= (3x^2)+(2/3)-1.5 0.3646045635 7.4166666667-1 1.4484840529 3.6666666667

-0.5 2.3616957835 1.41666666670 3 0.6666666667

0.5 3.4038863945 1.41666666671 3.7988864402 3.6666666667

1.5 4.6231634737 7.41666666672 6.5567624258 12.6666666667

2.5 10.5802067296 19.41666666673 18.10555193 27.6666666667

Tabla nª 02

3ª Opciòn

x y1 =2cos(x)-3x^2 Y2= ^(x)+(2/3)-�-1.5 -6.6085255967 0.4435365065-1 -1.9193953883 0.2987872255

-0.5 1.0051651238 0.0601360070 2 -0.3333333333

0.5 1.0051651238 -0.9820546041 -1.9193953883 -2.0516151618

1.5 -6.6085255967 -3.81502240372 -12.8322936731 -6.7223894323

2.5 -20.3522872311 -11.5158272943 -28.9799849932 -19.4188702565

Tabla nª 03

4ª Opciòn

x y1 =2cos(x)-(2/3) Y2= ^(x)+3x^2-�-1.5 -0.5251922633 6.5268698399-1 0.4139379451 2.6321205588

-0.5 1.0884984571 0.14346934030 1.3333333333 -1

0.5 1.0884984571 -0.89872127071 0.4139379451 0.2817181715

1.5 -0.5251922633 2.26831092972 -1.4989603398 4.6109439011

2.5 -2.2689538978 6.5675060393

3 -2.6466516599 6.9144630768Tabla nª 04

5ª Opciòn

x y1 = cosx Y2=( - ^(x)+(3x^2)+(2/3))/2 �-1.5 0.0707372017 2.4717682533

-1 0.5403023059 1.1493936127-0.5 0.8775825619 0.2800680035

0 1 -0.16666666670.5 0.8775825619 -0.241027302

1 0.5403023059 -0.02580758091.5 0.0707372017 0.3424887982

2 -0.4161468365 0.63880528392.5 -0.8011436155 0.492086353

3 -0.9899924966 -0.7094351283Tabla nª 05

6ª Opciòn

x y1 = ^(x) � Y2= -2cos(x)+(3x^2)+(2/3)-1.5 0.2231301601 7.2751922633

-1 0.3678794412 2.5860620549-0.5 0.6065306597 -0.3384984571

0 1 -1.33333333330.5 1.6487212707 -0.3384984571

1 2.7182818285 2.58606205491.5 4.4816890703 7.2751922633

2 7.3890560989 13.49896033982.5 12.1824939607 21.0189538978

3 20.0855369232 29.6466516599Tabla nª 06

7ª Opciòn

x y1 = 2/3 Y2= 2cos(x)-(3x^2) ^(x)+�-1.5 0.6666666667 -6.3853954365-1 0.6666666667 -1.5515159471

-0.5 0.6666666667 1.61169578350 0.6666666667 3

0.5 0.6666666667 2.65388639451 0.6666666667 0.7988864402

1.5 0.6666666667 -2.12683652632 0.6666666667 -5.4432375742

2.5 0.6666666667 -8.16979327043 0.6666666667 -8.89444807

Tabla nª 07

8ª Opciòn

x y1 = (3x^2) Y2= 2cos(x) ^(x)-(2/3)+�-1.5 6.75 -0.3020621032-1 3 0.7818173862

-0.5 0.75 1.69502911680 0 2.3333333333

0.5 0.75 2.73721972781 3 3.1322197735

1.5 6.75 3.956496807

2 12 5.89009575922.5 18.75 9.91354006293 27 17.4388852633

Tabla nª 08

9ª Opciòn

x y1 = 2 Y2= 3*(2cos(x)-(3x^2) ^(x))+�-1.5 2 -19.1561863095-1 2 -4.6545478413

-0.5 2 4.83508735050 2 9

0.5 2 7.96165918341 2 2.3966593206

1.5 2 -6.3805095792 2 -16.3297127225

2.5 2 -24.50937981123 2 -26.68334421

Tabla nª 09

10ª Opciòn

x y1 = x^2 Y2= (2*cos(x) ^(x)-(2/3))/3+�-1.5 2.25 -0.1006873677

-1 1 0.2606057954-0.5 0.25 0.5650097056

0 0 0.77777777780.5 0.25 0.91240657591 1 1.0440732578

1.5 2.25 1.3188322692 4 1.9633652531

2.5 6.25 3.30451335433 9 5.8129617544

Tabla nª 10

11ª Opciòn

x y1 = x Y2= raiz((2cos(x) ^(x)-(2/3))/3)+�-3 -3 Err:502-2 -2 Err:502

-1.5 -1.5 Err:502-1 -1 0.510495637

-0.5 -0.5 0.7516712750 0 0.8819171037

0.5 0.5 0.95519975711 1 1.0217990301

1.5 1.5 1.14840422722 2 1.4012013606

2.5 2.5 1.81783204793 3 2.4110084518

Tabla nª 11

12ª Opciònx y1 = x Y2= acos((3x^2-e^x+2/3)/2)

-1.5 -1.5 #VALUE!-1 -1 #VALUE!

-0.5 -0.5 1.15374311870 0 1.738244406

0.5 0.5 1.68708555171 1 1.0767497884

1.5 1.5 #VALUE!2 2 #VALUE!

2.5 2.5 #VALUE!3 3 #VALUE!

GRÀFICA Y LOCLIZACIÒN DE RAÌCES DE UNA ECAUCIÒN

Raiz

Existe una raiz

Existe uns raiz

-2 -1 0 1 2 3 4

-12

-10

-8

-6

-4

-2

0

2

4

y=cos(x) ^(x)-(2x^2)-(1/2)+�

-2 -1 0 1 2 3 40

5

10

15

20

25

30

Column B

Column C

Axis Title

Axis Title

-2 -1 0 1 2 3 4

-35

-30

-25

-20

-15

-10

-5

0

5

y1 =2cos(x)-3x^2

Y2= ^(x)+(2/3)-�

x

y

-2 -1 0 1 2 3 4

-4

-2

0

2

4

6

8

y1 =2cos(x)-(2/3) Y2= ^(x)+3x^2-�

x

y

-2 -1 0 1 2 3 4

-4

-2

0

2

4

6

8

y1 =2cos(x)-(2/3) Y2= ^(x)+3x^2-�

x

y

-2 -1 0 1 2 3 4

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

y1 = cosx Y2=( - ^(x)+(3x^2)+(2/3))/2 �

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

35

y1 = ^(x) � Y2= -2cos(x)+(3x^2)+(2/3)

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

35

y1 = ^(x) � Y2= -2cos(x)+(3x^2)+(2/3)

x

y

-2 -1 0 1 2 3 4

-10

-8

-6

-4

-2

0

2

4

y1 = 2/3 Y2= 2cos(x)-(3x^2) ^(x)+�

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

y1 = (3x^2) Y2= 2cos(x) ^(x)-(2/3)+�

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

y1 = (3x^2) Y2= 2cos(x) ^(x)-(2/3)+�

x

y

-2 -1 0 1 2 3 4

-30

-25

-20

-15

-10

-5

0

5

10

15

y1 = 2 Y2= 3*(2cos(x)-(3x^2) ^(x))+�

x

y

-2 -1 0 1 2 3 4-2

0

2

4

6

8

10

y1 = x̂ 2 Y2= (2*cos(x) ^(x)-(2/3))/3+�

X

Y

-4 -3 -2 -1 0 1 2 3 4

-4

-3

-2

-1

0

1

2

3

4

y1 = x Y2= raiz((2cos(x) ^(x)-(2/3))/3)+�

X

Y

-2 -1 0 1 2 3 4

-2

-1

0

1

2

3

4

y1 = x Y2= acos((3x̂ 2-e^x+2/3)/2)

X

Y

-2 -1 0 1 2 3 4-2

0

2

4

6

8

10

y1 = x̂ 2 Y2= (2*cos(x) ^(x)-(2/3))/3+�

X

Y

-2 -1 0 1 2 3 4

-2

-1

0

1

2

3

4

y1 = x Y2= acos((3x̂ 2-e^x+2/3)/2)

X

Y

GRÀFICA Y LOCLIZACIÒN DE RAÌCES DE UNA ECAUCIÒN

-2 -1 0 1 2 3 4

-12

-10

-8

-6

-4

-2

0

2

4

y=cos(x) ^(x)-(2x^2)-(1/2)+�

-2 -1 0 1 2 3 40

5

10

15

20

25

30

Column B

Column C

Axis Title

Axis Title

-2 -1 0 1 2 3 4

-35

-30

-25

-20

-15

-10

-5

0

5

y1 =2cos(x)-3x^2

Y2= ^(x)+(2/3)-�

x

y

-2 -1 0 1 2 3 4

-4

-2

0

2

4

6

8

y1 =2cos(x)-(2/3) Y2= ^(x)+3x^2-�

x

y

-2 -1 0 1 2 3 4

-4

-2

0

2

4

6

8

y1 =2cos(x)-(2/3) Y2= ^(x)+3x^2-�

x

y

-2 -1 0 1 2 3 4

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

y1 = cosx Y2=( - ^(x)+(3x^2)+(2/3))/2 �

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

35

y1 = ^(x) � Y2= -2cos(x)+(3x^2)+(2/3)

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

35

y1 = ^(x) � Y2= -2cos(x)+(3x^2)+(2/3)

x

y

-2 -1 0 1 2 3 4

-10

-8

-6

-4

-2

0

2

4

y1 = 2/3 Y2= 2cos(x)-(3x^2) ^(x)+�

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

y1 = (3x^2) Y2= 2cos(x) ^(x)-(2/3)+�

x

y

-2 -1 0 1 2 3 4-5

0

5

10

15

20

25

30

y1 = (3x^2) Y2= 2cos(x) ^(x)-(2/3)+�

x

y

-2 -1 0 1 2 3 4

-30

-25

-20

-15

-10

-5

0

5

10

15

y1 = 2 Y2= 3*(2cos(x)-(3x^2) ^(x))+�

x

y

-2 -1 0 1 2 3 4-2

0

2

4

6

8

10

y1 = x̂ 2 Y2= (2*cos(x) ^(x)-(2/3))/3+�

X

Y

-4 -3 -2 -1 0 1 2 3 4

-4

-3

-2

-1

0

1

2

3

4

y1 = x Y2= raiz((2cos(x) ^(x)-(2/3))/3)+�

X

Y

-2 -1 0 1 2 3 4

-2

-1

0

1

2

3

4

y1 = x Y2= acos((3x̂ 2-e^x+2/3)/2)

X

Y

-2 -1 0 1 2 3 4-2

0

2

4

6

8

10

y1 = x̂ 2 Y2= (2*cos(x) ^(x)-(2/3))/3+�

X

Y

-2 -1 0 1 2 3 4

-2

-1

0

1

2

3

4

y1 = x Y2= acos((3x̂ 2-e^x+2/3)/2)

X

Y

GRÀFICA Y LOCLIZACIÒN DE RAÌCES DE UNA ECAUCIÒN

x y=2cos(x) ^(x)-(3x^2)-(2/3)+�-1.5 -7.0520621032-1 -2.2181826138

-0.5 0.94502911680 2.3333333333

0.5 1.98721972781 0.1322197735

1.5 -2.7935031932 -6.1099042408

2.5 -8.83645993713 -9.5611147367

X1 X2 MEDIA-1.0000000 -0.5000000 -0.7500000-0.7500000 -0.5000000 -0.6250000-0.7500000 -0.6250000 -0.6875000-0.6875000 -0.6250000 -0.6562500-0.6875000 -0.6562500 -0.6718750-0.6875000 -0.6718750 -0.6796875-0.6875000 -0.6796875 -0.6835938-0.6835938 -0.6796875 -0.6816407-0.6816407 -0.6796875 -0.6806641-0.6816407 -0.6806641 -0.6811524-0.6816407 -0.6811524 -0.6813966-0.6813966 -0.6811524 -0.6812745-0.6813966 -0.6812745 -0.6813356-0.6813966 -0.6813356 -0.6813661-0.6813661 -0.6813356 -0.6813509

-2 -1 0 1 2 3 4

-12

-10

-8

-6

-4

-2

0

2

4

y=2cos(x) ^(x)-(3x^2)-(2/3)+�

y=2cos(x) ^(x)-(3x^2)-(2/3)+�

-0.6813509 -0.6813356 -0.6813433-0.6813509 -0.6813433 -0.6813471-0.6813509 -0.6813471 -0.6813490-0.6813509 -0.6813490 -0.6813500-0.6813500 -0.6813490 -0.6813495-0.6813500 -0.6813495 -0.6813498-0.6813500 -0.6813498 -0.6813499-0.6813500 -0.6813499 -0.6813500-0.6813500 -0.6813499 -0.6813500-0.6813500 -0.6813500 -0.6813500

X1 X2 MEDIA1.500000 1.000000 1.2500001.250000 1.000000 1.1250001.125000 1.000000 1.0625001.062500 1.000000 1.0312501.031250 1.000000 1.0156251.031250 1.015625 1.0234381.031250 1.023438 1.0273441.027344 1.023438 1.0253911.027344 1.025391 1.0263681.026368 1.025391 1.0258801.026368 1.025880 1.0261241.026368 1.026124 1.0262461.026368 1.026246 1.0263071.026368 1.026307 1.0263381.026338 1.026307 1.0263231.026338 1.026323 1.0263311.026331 1.026323 1.0263271.026331 1.026327 1.0263291.026331 1.026329 1.0263301.026331 1.026330 1.0263311.026331 1.026330 1.026331

primera raiz

F(X1) F(X2) F(X1)*F(X2) F© F(X1)*F© F(X2)*F©-2.2181826 0.945029117 -2.0962471564 -0.418422376 0.92813724 -0.395421329-0.4184224 0.945029117 -0.3954213286 0.318646001 -0.133328617 0.301129749-0.4184224 0.318646001 -0.1333286168 -0.036133946 0.015119252 -0.011513938-0.0361339 0.318646001 -0.0115139375 0.144706031 -0.0052288 0.046109998-0.0361339 0.144706031 -0.0052288 0.05514719 -0.001992686 0.007980131-0.0361339 0.05514719 -0.0019926856 0.009721732 -0.000351285 0.000536126-0.0361339 0.009721732 -0.0003512846 -0.013152352 0.000475246 -0.000127864-0.0131526 0.009721732 -0.0001278665 -0.001702014 0.000022386 -1.6547E-005-0.0017023 0.009721732 -1.65494E-005 0.004013074 -6.8315E-006 0.000039014-0.0017023 0.004013074 -6.83148E-006 0.001156223 -1.9682E-006 0.00000464-0.0017023 0.001156223 -1.96825E-006 -0.000272832 4.64443E-007 -3.1545E-007-0.0002731 0.001156223 -3.15793E-007 0.000441602 -1.2061E-007 5.10591E-007-0.0002731 0.000441602 -1.20612E-007 8.42519E-005 -0.000000023 3.72058E-008-0.0002731 8.39592E-005 -2.29313E-008 -9.4579E-005 2.58319E-008 -7.9408E-009-0.0000946 8.39592E-005 -7.94081E-009 -5.3092E-006 5.02143E-010 -4.4576E-010

-2 -1 0 1 2 3 4

-12

-10

-8

-6

-4

-2

0

2

4

y=2cos(x) ^(x)-(3x^2)-(2/3)+�

y=2cos(x) ^(x)-(3x^2)-(2/3)+�

-0.0000056 8.39592E-005 -4.70333E-010 3.91789E-005 -2.1948E-010 3.28943E-009-0.0000056 3.88862E-005 -2.17837E-010 1.66422E-005 -9.3228E-011 6.47151E-010-0.0000056 1.66422E-005 -9.32281E-011 5.52015E-006 -3.0923E-011 9.18673E-011-0.0000056 5.52015E-006 -3.09234E-011 -4.0881E-008 2.29013E-013 -2.2567E-013-0.0000003 5.52015E-006 -1.84134E-012 2.59329E-006 -8.6504E-013 1.43153E-011-0.0000003 2.59329E-006 -8.65036E-013 1.12986E-006 -3.7688E-013 2.93006E-012-0.0000003 8.37176E-007 -2.79254E-013 2.51805E-007 -8.3994E-014 2.10805E-013-0.0000003 2.51805E-007 -8.39937E-014 -4.0881E-008 1.36366E-014 -1.0294E-014-0.0000003 2.51805E-007 -8.39937E-014 -4.0881E-008 1.36366E-014 -1.0294E-014-0.0000003 -3.3357E-007 1.112670E-013 -3.3357E-007 1.11267E-013 1.11267E-013

segunda raiz

F(X1) F(X2) F(X1)*F(X2) F© F(X1)*F© F(X2)*F©-2.79350319 0.132219774 -0.3693563595 -1.233178984 3.44488943 -0.163050646-1.23317898 0.132219774 -0.163050646 -0.520971784 0.642451456 -0.068882771-0.52097178 0.132219774 -0.0688827713 -0.186410137 0.097114422 -0.024647106-0.18641014 0.132219774 -0.0246471061 -0.025033359 0.004666472 -0.003309905-0.02503336 0.132219774 -0.0033099051 0.054117256 -0.001354737 0.007155371-0.02503336 0.054117256 -0.0013547367 0.014671896 -0.000367287 0.000794003-0.02503336 0.014669363 -0.0003672234 -0.00514965 0.000128913 -7.5542E-005-0.00514965 0.014669363 -7.55421E-005 0.00476796 -2.4553E-005 6.99429E-005-0.00514965 0.00476796 -2.45533E-005 -0.000188821 9.72360E-007 -9.0029E-007-0.00019136 0.00476796 -9.12396E-007 0.002288807 -0.000000438 1.09129E-005-0.00019136 0.002286269 -4.37500E-007 0.001047581 -2.0046E-007 2.39505E-006-0.00019136 0.001047581 -2.00465E-007 0.000428142 -8.1929E-008 4.48514E-007-0.00019136 0.000428142 -8.19292E-008 0.000118399 -2.2657E-008 5.06917E-008-0.00019136 0.000118399 -2.26568E-008 -3.6478E-005 0.000000007 -4.3190E-009-3.902E-005 0.000118399 -4.61962E-009 3.96914E-005 -1.5487E-009 4.69943E-009-3.902E-005 3.71524E-005 -1.44959E-009 -9.3233E-007 3.63771E-011 -3.4638E-011-3.471E-006 3.71524E-005 -1.28968E-010 1.68406E-005 -5.8459E-011 6.25669E-010-3.471E-006 1.68406E-005 -5.84592E-011 6.68464E-006 -2.3205E-011 1.12573E-010-3.471E-006 6.68464E-006 -2.32046E-011 1.60666E-006 -5.5772E-012 1.07400E-011-3.471E-006 1.60666E-006 -5.57724E-012 -9.3233E-007 3.23642E-012 -1.4979E-012-3.471E-006 1.60666E-006 -5.57724E-012 -9.3233E-007 3.23642E-012 -1.4979E-012

x y=2cos(x) ^(x)-(3x^2)-(2/3)+�-1.5 -7.0520621032

-1 -2.2181826138-0.5 0.9450291168

0 2.33333333330.5 1.9872197278

1 0.13221977351.5 -2.793503193

2 -6.10990424082.5 -8.8364599371

3 -9.5611147367

metoto regula falsi a b-0.800000 -0.600000-0.800000 -0.675675-0.800000 -0.680972-0.800000 -0.681325-0.800000 -0.681348-0.800000 -0.681350-0.800000 -0.681350-0.800000 -0.681350-0.800000 -0.681350

a b1.200000 1.0000001.200000 1.0246211.200000 1.0262211.200000 1.026323

-2 -1 0 1 2 3 4

-12

-10

-8

-6

-4

-2

0

2

4

y=2cos(x) ^(x)-(3x^2)-(2/3)+� Column C

primera raizc f(a) f(b) f(a)*f(b) f© f(a) *f©

-0.675675 -0.743924 0.452816 -0.336861 0.033106 -0.024629-0.680972 -0.743924 0.033106 -0.024628 0.002212 -0.001646-0.681325 -0.743924 0.002212 -0.001645 0.000147 -0.000109-0.681348 -0.743924 0.000146 -0.000109 0.000010 -0.000007-0.681350 -0.743924 0.000011 -0.000008 0.000001 -0.000001-0.681350 -0.743924 0.000000 0.000000 0.000000 0.000000-0.681350 -0.743924 0.000000 0.000000 0.000000 0.000000-0.681350 -0.743924 0.000000 0.000000 0.000000 0.000000-0.681350 -0.743924 0.000000 0.000000 0.000000 0.000000

segunda raizc f(a) f(b) f(a)*f(b) f© f(a) *f©

1.024621 -0.941834 0.132220 -0.124529 0.008675 -0.0081711.026221 -0.941834 0.008674 -0.008169 0.000553 -0.0005211.026323 -0.941834 0.000555 -0.000523 0.000035 -0.0000331.026330 -0.941834 0.000037 -0.000035 0.000002 -0.000002

-2 -1 0 1 2 3 4

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0

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y=2cos(x) ^(x)-(3x^2)-(2/3)+� Column C

f(b) *f©0.0149910.0000730.0000000.0000000.0000000.0000000.0000000.0000000.000000

f(b) *f©0.0011470.0000050.0000000.000000

x y=2cos(x) ^(x)-(3x^2)-(2/3)+�-1.5 -7.0520621032-1 -2.2181826138

-0.5 0.94502911680 2.3333333333

0.5 1.98721972781 0.1322197735

1.5 -2.7935031932 -6.1099042408

2.5 -8.83645993713 -9.5611147367

METODO DE NEWTONPRIMERA RAIZi X0

0 -0.751 -0.6839574052 -0.6813540223 -0.681349943

SEGUNDA RAIZi X0

0 11 1.026632192 1.0263303543 1.026330316

-2 -1 0 1 2 3 4

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y=2cos(x) ^(x)-(3x^2)-(2/3)+�

y=2cos(x) ^(x)-(3x^2)-(2/3)+�

OK

F(x)=2*cos(x) ^(x)-(3x^2)-(2/3)+� F'(x)= -2sen(x) ^(x)-6(x)+�-0.4184223762 6.3356440728

-0.015287301 5.8720910204-2.38772773505369E-005 5.85374621379.48258138677716E-011 5.8537174669

F(x)=2*cos(x) ^(x)-(3x^2)-(2/3)+� F'(x)= -2sen(x) ^(x)-6(x)+�0.1322197735 -4.9646601412

-0.0015331028 -5.0792655328-1.90945567468681E-007 -5.0779844088

0.000000002 -5.0779842475

-2 -1 0 1 2 3 4

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y=2cos(x) ^(x)-(3x^2)-(2/3)+�

y=2cos(x) ^(x)-(3x^2)-(2/3)+�

-0.41842238 -0.99101119X1= X0-((f(x0)/f'(x0)) 40.1403858

-0.6839574049-0.6813540222

-0.681349943-0.681349943

X1= X0-((f(x0)/f'(x0)) 0.13221977 2.177979521.0266321903 24.64785031.02633035451.02633031641.0263303164

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y=2cos(x) ^(x)-(3x^2)-(2/3)+�

y=2cos(x) ^(x)-(3x^2)-(2/3)+�

0.01033028 OK

0.01168345 OK

-2 -1 0 1 2 3 4

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0

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y=2cos(x) ^(x)-(3x^2)-(2/3)+�

y=2cos(x) ^(x)-(3x^2)-(2/3)+�