Tarea 12 Euler

eLClGR_PF94 9 8

 

Vgrhg 72. Huehr 

Chtlfls Muchrk`ls Kk (Kmstktutl _lektë`mk`l Mg`klmge)

PtuFl`u ml hstç pgtrl`kmgfl mk gvgegfl plr mkmiñm `lehikl l umkvhrskfgf.

Fhs`grigfl plr cgrkgmg rkls (ahssk`gcgils8 (ahssk`gcgils8Oicgke.`lc) Oicgke.`lc)

eLClGR_F94 9 8

 

VGRHG CËVLFL FH HXEHR

_rlbehcg 7 

Eg vhel`kfgf fh nlrcg`kðm fhe JLD hm eg rhg``kðm1 2 J2@r2L9  + 2 D2L + 0 P

6 JLD + 2 @r2L0 + 0 PL2 

hstç fgfg plr eg h`ug`kðm `kmëtk`g1

 3 .−       (   )     

hm eg `uge x hs he mñchrl fh clehs fh JLD nlrcgfgs y t hs he tkhcpl hm shiumfls. @ge`ueh he mñchrl fh clehs kmk`kgehs fh P (m0) rhquhrkfgs pgrg nlrcgr 78.7 clehs fh JLD hm he tkhcpl t 3 ?.2 shiumfls. Egs clehs kmk`kgehs fh J 2@r2L9 y D2L (m7)  y (m2) slm 74?? clehs gcbgs. Vlch um pgsl fh kmthirg`kðm d 3 ?.?8 shiumfls usgmfl he Cëtlfl fh Huehr. Pleu`kðm1 m 0 329>? clehs Puplmhr m0329?? t3? x3? t3?.?8 x`ge`uegfg 37.2 t3 ?.7 x3 0.?6 t3?.78 x38.> t3?.2 x376.4

Puplmhr m0324??

V3? x3? V3?.?8 x39.4 V3?.?8 T3;.7 V3?.78 x37?.2 V3?.2 x37> 7

Fhs`grigfl plr cgrkgmg rkls (ahssk`gcgils8Oicgke.`lc) eLClGR_F94 9 8

 

Puplmhr m03 29>? V3? x3? V3?.?8 x3 0.6728 V3?.7 x3 8.> V3?.78 x3 9.4 V3?.2 x378.?426  _RLBEHCG 7 d

t

x

y'

?.?8

?

?

9>.0

?.?8

0.4

98.4

?.7

9.>

98.0

?.78

77.6

96.4

?.2

78.7

96.6

?.28

74.4

90.;

?.0

22.8

90.8

?.08 ?.6

2>.2 2;.;

90.? 92.>

?.68

00.8

92.2

?.8

09.7

97.9

Nlrcg`kðm fh JLD ;? 4? 9?    D    L>?    J    h     f 8?    s 6?    h     e

y 3 -;.6?70x + 9>.2>7 R² 3 7

   l

   C0?    #

2? 7? ?

y 3 98.886x + ?.?209 R² 3 7 ?

?.?8

?.7

?.78

?.2

?.28

Vkhcpl (s)

n(x)

fy/fx

Ekmhgr (n(x))

Ekmhgr (fy/fx)

2

Fhs`grigfl plr cgrkgmg rkls (ahssk`gcgils8Oicgke.`lc) eLClGR_F94 9 8

 

 

_rlbehcg 2

Rhsuhevg he skiukhmth prlbehcg fh vgelr kmk`kge `lm he Cëtlfl fh Huehr1  −

3

   _^K



 

 y(7) 3 6.2  y(0) 3 <

Xsh um pgsl fh kmthirg`kðm d 3 7

_RLBEHCG 2 d

t

y

y'

7

7

6.2

-9.6

2

-0.2

9.2

0

6.?

>.0

6

7?.0

7?.4

8

27.2

7>.8

>

09.9

20.6

9

>7.7

07.8

4

;2.9

6?.4

;

700.8

87.0

7?

746.4

>0.?

77

269.;

98.;

  dgrt Vkteh 7? 4 > 6 2 ? -2 ?

?.8

7

7.8

2

2.8

0

0.8

-6 -> -4 -7? n(x)

fy/fx

0

Fhs`grigfl plr cgrkgmg rkls (ahssk`gcgils8Oicgke.`lc) eLClGR_F94 9 8

 

_rlbehcg 0

Xmg bgrrhrg fh prlth``kðm sh sktñg ge nkmge fh um `kr`uktl `lm he lbahtkvl fh pgrgr `l`dhs quh dgm phrfkfl he `lmtrle. Hstg bgrrhrg sh dg fksh÷gfl fh tge tg e nlrcg quh eg nuhrzg quh eg bgrrhrg gpek`g ge `l`dh hstç fgfg fg fg hm num`kðm fh eg vhel`kfgf v y fhe fhspegzgckhmtl x fh eg pgrth nrlmtge fh eg bgrrhrg fh g`uhrfl g eg skiukhmth hxprhskðm1

N 3 Jv 0 (x+7) 0  

Flmfh J 3 0? Ji s/c8 hs umg `lmstgmth. Xm `l`dh `lm umg cgsg c 3 78?? Ji sh kcpg`tg `lmtrg eg bgrrhrg fh prlth``kðm g umg vhel`kfgf fh ;? Jc/d. @ge`ueh eg vhel`kfgf quh thmfrç he `l`dh fhspuës fh dgbhrsh kcpg`tgfl `lmtrg eg bgrrhrg y rh`lrrkfl umg fkstgm`kg fh 0 c. Eg fhsg`hehrg`kðm fhe `l`dh fhspuës fh `dl`gr `lmtrg eg bgrrhrg hstç fgfg plr eg Phiumfg Ehy fh Mhwtlm1 cg 3 -Jv 0 (x+7) 0  

Flmfh eg g`hehrg`kðm hstç fgfg plr1

+  3    Eg vhel`kfgf hstç fgfg hm num`kðm fh x plr eg skiukhmth hxprhskðm1 v fv 3 g fx

Fh flmfh1

 3 +    Wuh hs eg h`ug`kðm fknhrhm`kge f knhrhm`kge plr rhslevhr. Gpekquh he Cëtlfl fh Huehr y utkek`h um pgsl fh kmthirg`kðm d 3 ?.8 chtrls. Pleu`kðm1 v(0)3?.8 c/s

6

Fhs`grigfl plr cgrkgmg rkls (ahssk`gcgils8Oicgke.`lc) eLClGR_F94 9 8

 

_LRBEHCG 0 d

x

y

y'

?.8

?

28

-72.8

?.8

74.98

-20.90

7

>.44

-9.84

7.8

0.?;

-2.;;

2

7.>?

-7.04

2.8

?.;7

-?.97

0

?.88

-?.0;

0.8

?.0>

-?.20

6

?.26

-?.78

6.8 8

?.79 ?.72

-?.?; -?.?>

^hel`kfgf ^hel `kfgf fhspuhs fhe kcpg`tl 78? 7??    s 8?     /    c ?     f    g     f ?    k    ` -8?    l     e    h    ^-7??

?.8

7

7.8

2

2.8

0

0.8

-78? -2??

fkgtm`kg c

n(x)

fy/fx

8

Fhs`grigfl plr cgrkgmg rkls (ahssk`gcgils8Oicgke.`lc)