Soal Penilaian Harian Kunci Dan Pedoman Penskoran

 

F^]JV YLDE [NCJEDJDC @DVJDC MDVJCO Hnradhdc slde-slde fnrjhut jcj mncodc fdjh mdc fncdr.

4.

Mdnr Mdnrd` d` ydco ydco bnb bnbnc ncu` u`jj sjstnb stnb pnrt pnrtjjmdhs mdhsdb dbdd ddc c ( 6 x +  y ’ = )( 6 x + 9  y ’ 7 ) ≭ ; , x ≮ ; ,  md mdc  y ≮ ; dmded`…

6.

[n [nrr`dtjhdc od odbfdr fn fnrjhut. Z ? =

6

9

>>

P

0

Yjstnb pnrtjmdhsdbddc ydco bnbncu`j mdnrd` ydco mjdrsjr dmded`… 9.

^ctu ^ctuh h bncdbf bncdbfd` d` pnco`d pnco`dsj sjed edc, c, snlrd snlrdco co jfu sntjd sntjdp p `d `drj rjcyd cyd bn bnbp bprl rlmu muhs hsjj mud ancjs ancjs hun uctuh  uctuh  mjaude. Yntjdp ancjs hun ancjs J blmdecyd Vp 6;;,;; mncodc hnuctucodc =;%, snmdcohdc sntjdp  ancjs hun ancjs JJ blmdecyd Vp 9;;,;; mncodc hnuctucodc 9;%. Blmde ydco tnrsnmjd sntjdp `drjcyd Vp 4;;.;;;,;; mdc pdejco fdcydh `dcyd mdpdt bnbprlmuhsj =;; hun. Fudted` blmne bdtnbdtjhd mdrj pnrbdsded`dc tnrsnfut.

{

( 6 x + y ∖ = ) ( x + 6 y ∖> ) ≭ ;

=.

Mjfn Mjfnrrjhdc jhdc sj sjstnb stnb pnr pnrtj tjmd mdhs hsdb dbdd ddc c

 x ≮ ;  y ≮ ;

.

Mncodc bncooucdhdc bntlmn odrjs snejmjh, cjedj bjcjbub gucosj g  ( x , y )29 x + 6 y  mdrj sjstnb  pnrtjmdhsdbddc tnrsnfut dmded`… >.

Vdhd dmde dmded` d` rnsnee rnsneenr nr hdls hdls snpdhfl snpdhfled ed Drsnc Drsncde de mdc mdc Fdrine Fdrinelcd lcd.. Fnrmdsd Fnrmdsdrhd rhdc c hnfjadh hnfjadhdc dc donc, donc, Vdhd Vdhd `dcyd flen` bnbnsdc hdls Drsncde 4;; sdbpdj mncodc 4>; pltlco, snmdcohdc tlhl Vdhd `dcyd sdcooup sdc ooup bncaude bncaude =;; pltlco pltlco hdls. hdls. Dh`jrcy Dh`jrcydd Vdhd Vdhd bnbutu bnbutushd shdc c uctuh uctuh bnbnsd bnbnsdc c 49; hdls Drsncde mdc sjsdcyd hdls Fdrinelcd. Ajhd hnuctucodc mdrj hdls Drsncde mdc hdls Fdrinelcd dm dmde ded` d` Vp.4 Vp.4;. ;.;; ;;;, ;,;; ;; md mdc c Vp. Vp. ?. ?.;; ;;;, ;,;; ;;,, dp dpdh dhd` d` hn hnpu putu tusd sdc c Vdhd Vdhd sumd sumd` ` tn tnpd pdtt uctu uctuh  h  bncolptjbdehdc hnuctucodc< Anedshdc dedsdcbu.

 

[NMLBDC [NCYHLVDC Cl

Ylde

.

Hucij Adwdfdc

Mdnr Md nrd` d` yd ydco co bnbn bnbncu cu`j `j sj sjst stnb nb

(6 x +  y ’ = )( 6 x + 9 y ’ 7 )≭ ; 

 pnrtjmdhsdbddc1

Y[tEMW ydco tnradmj1

(6 x +  y ’ = )( 6 x + 9 y ’ 7 )≭ ; , x ≮ ; ,

=

+  y ≭ =  6  x +  y ≮ = 4 6 6 x + 9  y ≮ 7 … ( )  dtdu 6 x + 9  y ≭ 7 … ( )  6  x

{

mdc  y ≮ ;  dmded`…

Yhlr

{

 x ≮ ; mdc  y ≮ ;  drtjcyd mdnrd` pncynensdjdc fnrdmd mj snfned` hdcdc subfu Z mdc mjdtds subfu P. Yn`jcood mdnrd` pncynensdjdc mdrj hnmud sjstnb

6

 pnrtjmdhsdbddc tnrsnfut mjpnrlen`1

4

Z =

Mdnrd` 4

6

=

Mdnrd` 6 P 6

 

9

Yhlr slde 4 [nr`dtjhdc odbfdr fnrjhut.

4;

Z

Z

?

?

=

= 6

6

6 9 9

Yjst Yjstnb nb

>>

pnr pnrtjmd tjmdhs hsdb dbdd ddc c

0

>>

0

P

>

P

Yjstnb pnrsdbddc odrjs pnbfdtds1 ydco ydco

(j) Yubfu  P ↖ y 2;

bnbn bn bncu cu`j `j mdnr mdnrd` d` yd ydco co mjdr mjdrsj sjr  r  (jj) Yubf Yubfu u Z ↖ x2 ; dmded`…

(jjj) (jjj) Odrjs Odrjs h ↖ = x + 9  y 246 (jv) (jv) Odrj Odrjss e ↖ 6 x + >  y 24; (v) Odrjs b ↖ ? x + 0 y 2>7 Y[tEMW1 

  y ≮ ;  (mj hdcdc subfu Z)

>

 



  x ≮ ; (mj hdcdc subfu P) Hdrn Hd rncd cd dm dmdd mud md mdnr nrd` d` ydco ydco mj mjdr drsj sjr, r, bdhd bdhd



(jjj)x(jv), mjpnrlen`1

( = x +9  y ∖46 ) (6 x +> y ∖4; ) ≮ ;  Hdrncd mdnrd` ydco mjdrsjr1  fdwd` ß fdwd`¼ ¼ dtds ß dtds ¼ ¼ sn`jcood tdcmdcyd ≮ 

  ? x

+ 0 y ≭ >7 (mj fdwd` odrjs)

Ad Admj mj,, Yjst Yjstnb nb pn pnrt rtjm jmdh dhsd sdbd bddc dc yd ydco co bnbn bnbncu cu`j `j mdnrd` ydco mjdrsjr dmded`1

( = x +9 y ∖46 ) ( 6 x +>  y ∖4; ) ≮ ;   ? x + 0 y ≭ >7,  x ≮ ;  mdc  y ≮ ; .

Yhlr slde 6 ^ctuh bncdbf ^ctuh bncdbfd` d` pnco`ds pnco`dsjed jedc, c, snlrdco jfu sntjdp `drjcyd

4;

Ancjs Hun

Blmde

mjau mjaude de.. Yn Yntj tjdp dp an ancj cjss hu hunn an ancj cjss J

Hun J Hun JJ [nrsnmjdd

6.;;; 9.;;; 4.;;;.;;;

blmd bl mdec ecyd yd

c

bnbprlmuhsj mud ancjs hun uctuh 

Vp 6; 6;;; ;;,; ,;; ;

mn mnco codc dc

Fdcydh  ^ctuco Hun 4 =;% ↖0;; 4 9;% ↖:;; =;;

>

hnuctucodc =;%, snmdcohdc sntjdp  ancjs hun ancjs JJ blmdecyd Vp 9

9;;;,;; mncodc hnuctucodc 9;%. Blmde ydco tnrsnmjd sntjdp `drjcyd

Bjsde1 Hun J 1  x  mdc hun JJ1  y Gucosj hncmded1

pdejco Blmde 1 6.;;; x + 9.;;; y ≭ 4.;;;.;;;  dtdu 6 x + 9  y ≭ 4;;;      fdcydh `dcyd mdpdt bnbprlmuhsj Fdcydh hun 1  x + y ≭ =;; =;; hun. Fudted` blmne Vp

4.; 4.;;;.;; ;;; ;,;;

bdtn bd tnbd bdtj tjhd hd

mdrj mdrj

mdc

pn pnrb rbds dsde ded` d`dc dc

tnrsnfut. =

Mjfnr nrjjhd hdc c sjstnb pnrtjmdh dhssdbddc

Gucosj tuaudc1 g  ( ( x . y ) 20;; x + :;;  y Hncmded clc cnodtjg 1  x ≮ ; mdc  y ≮ ; Yhlr slde 9 Mdnrd` pncyn yneensdjdc mdrj sjstnb pnr nrttjmdhsdbddc dc11

9

6 4; =

 

{

( 6 x + y ∖ = ) ( x + 6 y ∖> ) ≭ ; . Mncodc

 x ≮ ;  y ≮ ;

bncooucdhdc snej snejmj mjh, h,

cjed cjedjj

bntlmn

odrjs

bjcj bjcjbu bub b

guco gucosj sj

g  ( x , y )29 x + 6 y  

mdrj

sjstnb

 pnrtjmdhsdbddc tnrsnfut dmded`…

Odrjs snejmjh1 9 x + 6 y 27

(hnt1 Ordgjh mjpnrlen` mncodc onlonfrd) Mnco Mn codc dc bnco bncoon onsn snrr od odrj rjss sn snej ejmj mjh h hn hndr drd` d` hj hjrj rj (tnrmn (tn rmnhdt hdt mdrj mdrj tj tjtjh tjh (;,;)) (;,;)) bdhd bdhd mjpnrl mjpnrlen` en` tjt tjtjh  jh  bjcjbu bjc jbub b mdrj mdrj mdnrd` mdnrd` pncynen pncynensdj sdjdc dc dmded` dmded` tjt tjtjh  jh 

9

(;,6.>). Admj, cjedj bjcjbub bjcjbub mdrj sjstnb sjstnb pnrtjmdhsdb pnrtjmdhsdbddc ddc

Vdhd

dmded`

rnsneenr

tnrsnfut dmded` g  ( ( ;,6.> )2 9 ( ; ) + 6 ( 6.> )2> Yhlr Ylde = hdls Bjsde1

9 4;

snpdhfled Drsncde mdc Fdrinelcd.  x  1 fdcydhcyd hdls Drsncde  y 1 Fnrmdsdrhdc Fnrmds drhdc hnfjadhdc donc, Vdhd  y  1 fdcydhcyd hdls Fdrinelcd `dcyd

flen`

bnbnsdc

hdls Blmne bdtnbdtjhd1

Drsncd Drs ncdee 4;; sdbpdj sdbpdj mncodc mncodc 4>;  x + y ≭ =;;    pltlco, `dcyd >

 pltlco

snmdcohdc sdcoo oou up hdls.

tlhl

bncaude Dh`jrcyd

Vdhd 4;; ≭ x ≭ 4>;   =;;

6>; ≭

y ≭ 9;;

Vdhd Gucosj lfanhtjg1 g  ( ( x , y )24;.;;; x + ?.;;;  y

bnbutushdc uctuh bnbnsdc 49;

6

hd hdls ls Drsn Drsncd cdee md mdc c sj sjsd sdcy cydd hd hdls ls Fdrine Fdr inelcd lcd.. Ajhd Ajhd hnuctuc hnuctucodc odc mdrj mdrj hdls Drsncde mdc hdls Fdrinelcd dmde dmded` d`

Vp.4 Vp.4;. ;.;; ;;;, ;,;; ;;

mdc mdc

Vp.

?.;;;,;;, dpdhd` hnputusdc Vdhd sumd` tnpdt uctuh bncolptjbdehdc hnuctucodc< Anedshdc dedsdcbu. >

Mdnrd` pncynensdjdc1

6

 

(hnt1 Ordgjh mjpnrlen` mncodc onlonfrd) Mdrj mdnrd` pncynensdjdc mjpnrlen` tjtjh plalh1 (4;;,6>;), (4>;,6>;) mdc (4;;,9;;) ^aj tjtjh plalh pdmd gucosj lfanhtjg1 ]jtjh [lalh    g  ( ( x , y )2 4;.;;; x + ?.;;;  y (4;;,6>;)   6.?>;.;;; (4>;,6>;)   9.6>;.;;; (4;;,9;;)   9.4;;.;;; Fnrmds Fnr mdsdrh drhdc dc tdfne, tdfne, mjpnrl mjpnrlen` en` cje cjedj dj bdhsjb bdhsjbub ub

6

6

>;.;;;   .9.6 >;.;;; Hnputusdc Hnputu sdc Vdhd bnbnsdc bnbnsdc 49; hdls Drsncde Drsncde mdc

sjsdcyd hdls Fdrinelcd1

g   (( 49;,6?; ) 29.4:;.;;;  

6

Admj, hnputusdc Vdhd hurdco tnpdt, hdrncd fneub bncolptjbdehdc hnuctucodc. Yhlr slde > ]ltde Yhlr

Cjedj dh`jr 2

Aube Aubed`Yhl d`Yhl r Nssd Nssdyy >;

ß 4;;

Ajhd HHB ?0, bdhd hrjtnrjd pncjedjdc dmded`1 D (Ydcodt fdjh)

1 Dpd pdf fjed sjswd bnbpnr nrl len` :6 ≭ C D ≭ 4;; 

F (Fdjh)

1 Dpdfjed sjswd bnbpnrlen` 0> ≭ CD 5 :6

I (Iuhup) M (Hurdco)

1 Dpdfjed sjswd bnbpnrlen` ?0 ≭ CD 5 0> 1 Dpdfjed sjswd bnbpnrlen`  CD 5 ?0

4; >;

 

Mncodc  CD  dmded` cjedj dh`jr 

`ttps1//glrbs.oen/iyl7=jM7>r4IHZ`V7)) ]dbpjedc mdedb Olloen Glrb  (`ttps1//glrbs.oen/iyl7=jM7>r4IHZ`V7

 Edbpjrdc

[VLOVDB VNBNMJ

Ynhled` Hneds/Ynbnstnr Bdtd [nedadrdc ^edcodc @drjdc hn]dcoode ^e ^edcodc @d @drjdc Fnctuh ^edcodc @drjdc

1 YBD Cnonrj 4 Ijedbdyd 1 PJ ............/4 1 Bdtnbdtjhd 1 ........ 1 .......... 1 .........

 

Bdtnrj ^edcodc @drjdc HM/Jcmjhdtlr HHB

1 ........ 1 ......... 1 .........

 Cl. Cdbd [nsnrtd mjmjh

Cjedj Jcmjhdtl ^edcodc r ydco  fneub mjhudsdj

Fnctuh  Cjedj tjcmdhdc sntned` rnbnmjd rnbjmjde e

Hntnrdcodc

4 6 9 = > 7 ? 0 : 4; 44 46 Mst d. [ncodyddc Ouru bnbfnrjhdc cdsj`dt dodr tntdp rncmd` `dtj, hdrncd tned` bncidpdj HHB (Hrjtnrjd Hntuctdsdc Bjcjbde) bdtnrj Bncnctuhdc Mdnrd` @jbpucdc [ncynensdjdc mdrj [nrtjmdhsdbddc Ejcndr Mud Wdrjdfne.

 Edbpjrdc

4. Hj Hjsj sj-h -hjs jsjj Ylde Ylde Vnb Vnbnm nmjd jdee  Cl

4

Hlbpntncsj Mdsdr Mdsdr 9.6 Bncanedshdc  prlordb ejcndr mud vd vdrj rjdf dfne ne md mdc c bntl bntlmn mn  pncynensdjdccyd mncodc

Bdtnrj

[rlordb Ejcndr 

Jcmjhdtlr Yld Yldee Mjfnrjhdc sjstnb  pnrtjmdhsdbddc  pnrtjmdhsdbdd c ejcndr mud vdrjdfne, pnsnrtd mjmjh mdpdt bncnctuhdc

Vdcd` Hlocjtjg 

 Cl Ylde

Fdctuh  Ylde

4

^rdjdc

I9 (Bncodpejhdsjhdc ) E9

 

bncooucdhdc bncooucdhd c bdsd bdsded` ed` hlctnhstude.

mdnrd` pncynensdjdc mdrj sjstnb pnrtjmdhsdbddc ejcndr mud vdrjdfne tnrsnfut. Mjfnrjhdc odbfdr mdnrd` `jbpucdc pncynensdjdc,  pnsnrtd mjmjh mdpdt mdpdt bncnctuhdc sjstnb

=.6 =.6 Bnc ncyn yneens nsdj djhd hdc c bd bdsd sded ed` ` hl hlct ctnh nhst stud udee ydco fnrhd fnrhdjtdc jtdc mncod mncodc c  prlordb ejcndr mud vdrjdfne.

6

[rlordb Ejcndr 

 pnrtjmdhsdbdd  pnrtjmdhsdbddc c ejcndr mud vdrjdfne ajhd mjhntd`uj mdnrd`  pncynensdjdccyd. Mjfnrjhdc slde inrjtd tnctdco bdsded` hlctnhstude ydco  fnrhdjtdc mncodc  pnrtjmdhsdbddc  pnrtjmdhsdbdd c ejcndr mud vdrjdfne, pnsnrtd mjmjh mdpdt bnbfudt blmne pnrtjmdhsdbddc mdrj bdsded` tnrsnfut

I= (Bncodcdejsjs)

6

^rdjdc

9

^rdjdc

E9

I9 (Bncnrdphdc) E6

 

 Edbpjrdc

4. Futj Futjrr Ylde Ylde mdc mdc Hucij Hucij Adw Adwdfd dfdc c  Cl.slde Ylde ^rdjhdced` edcohd`-edcohd` 4.

Hucij Adwdfdc Yjstnb pnrtjmdhsdbddccyd dmded`1  x + y ≭ 9 

mdedb bncoodbfdr ordgjh  pncynensdjdc mdrj sjstnb sjstnb

6 x

 pnrtjmdhsdbddc x + y ≭ 9, 6x + y ≭ 7 mdc x ≮ ; 8 y ≮ ;

Yhlr 

6

+ y ≭ 7 

 x ≮ ; mdc  y ≮ ;  drtjcyd mdnrd`  pncynensdjdc fnrdmd mj snfned` hdcdc subfu Z mdc mjdtds subfu P. Yn`jcood mdnrd` pncynensdjdc mdrj

6

hnmud sjstnb pnrtjmdhsdbddc tnrsnfut mjpnrlen`1

=

9.

[nr`dtjhdc odbfdr fnrjhut

Z y  0 >

   

;

N

0

4;

x

 

0

 

>

 

;

0

 

4; h

x e

Yjstnb pnrsdbddc odrjs pnbfdtds1 ]nctuhdc sjstnb  pnrtjmdhsdbddc mdrj mdnrd` mdnrd`  pncynensdjdc sjstnb sjstnb  pnrtjmdhsdbddc ejcndr ejcndr mj dtds

(j) Yubfu  P ↖ y 2; (jj (jj) Yub Yubfu Z ↖ x 2 ;

4

(jjj) (jjj) Odrjs Odrjs h ↖ 0 x + 0 y 2 7=

4

(jv) (jv) Odrj Odrjss e ↖ > x + 4; y 2>;

4

Y[tEMW1 



4   y ≮ ;  (mj hdcdc subfu Z)   x ≮ ; (mj dtds subfu P)

4

 

sn`jcood tdcmdcyd ≮ 

  x + y ≭ 0 (mj fdwd` odrjs)



  x + 6 y ≭ 4; (mj fdwd` odrjs)

Admj, Yjstnb pnrtjmdhsdbddc ydco

4

6

bnbncu`j mdnrd` ydco mjdrsjr dmded`1  x + y ≭ 0  x + 6 y ≭ 4; , =.

]nctuhdc blmne bdtnbdtjhd mdc mdnrd` `jbpucdc pncynensdjdc mdrj bdsded` fnrjhut 1 Fu Dcj Bnbfnej 46 ho hdidco uctuh mjaude edoj mdedb mud bdidb hnbdsdc hnije, ydjtu hnbdsdc ancjs D mdc ancjs F,  fnrturut-turut fnrjsj fnrjsj fnrdt fnrsj` hdidco 4;; o mdc 4>; o.

6

  x ≮ ;  mdc  y ≮ ; . [nrtdcyddc 1 fdodjbdcd bnblmnehdc bdsded` tnrsnfut hn mdedb fnctuh

4

 pnrtjmdhsdbddc< Ytrdtnoj mncodc pnrbjsdedc Bjsde Hdidco ancjs D 2 x

4

Hdidco ancjs F 2 y 46 ho 2 46;;; o Ancjs D 4;; o

Ancjs F 4>; o

[nrsnmjddc 46;;; o

6

Bdhd 4;;x + 4>;y ≭ 46;;; ]dcmd ≭ bncucauhhdc aubed`  pnrsnmjddc ydco tjmdh bnenfj`j 46 ho 4;;x + 4>;y ≭ 46;;; (mjsnmnr`dcdhdc mncodc bnbfdoj >;) 6x + 9y ≭ 6=; 6

6

Yhlr ]ltde

67

 

Cjedj dh`jr 2

Aubed` Aube d` Yhlr Yhlr yo mjpnr mjpnrlen` len` sjswd sjswd   ß 4;; Yhlr]ltde

Ajhd HHB ?0, bdhd hrjtnrjd pncjedjdc dmded`1 D (Ydcodt fdjh)

1 Dpd pdf fjed sjswd bnbpnr nrl len` :6 ≭ C D ≭ 4;; 

F (Fdjh)

1 Dpdfjed sjswd bnbpnrlen` 0> ≭ CD 5 :6

I (Iuhup)

1 Dpdfjed sjswd bnbpnrlen` ?0 ≭ CD 5 0>

M (Hurdco)

1 Dpdfjed sjswd bnbpnrlen`  CD 5 ?0

Mncodc  CD  dmded` cjedj dh`jr   Edbpjrdc

 

 Edbpjrdc [ncodyddc [rlordb Ejcndr

4. ]nctuhdc ]nctuhdc mdnrd` mdnrd` `jbpucdc `jbpucdc pncynens pncynensdjdc djdc mdr mdrjj sjstnb 6 x + y ≭ =

 x +  y ≭9

 

pnrtjmdhsdbddc

{

 x

+=

 y

≮=

 

6. Mdnrd` Mdnrd` ydco mjdrsjr pdmd odbfdr odbfdr mj fdwd` fdwd` bnrupdhdc bnrupdhdc `jbpucdc pncynensdjdc pncynensdjdc sjstnb pnrtjmdh pnrtjmdhsdbddc sdbddc.. ]nctuhdc sjstnb pnrtjmdhsdbddc mdrj mdnrd` tnrsnfut.

y 46

>

L

6

=

x

9. ]nctuhdc mdnrd` pncynensdjdc mdrj mdrj sjstnb pnrtjmdhsdbddc pnrtjmdhsdbddc ejcndr x + y ≭ 6> 8 6x + y ≭ 40 8 x ≮ ; 8 y ≮ ;. ;. =. Ynlrdco Jfu bnbpucydj 47; ordb bnctnod mdc 6=; ordb tnpuco tnrjou uctuh bnbfudt 6 ancjs

edpjs enojt mdc frlwcjns. Yntjdp hun edpjs enojt bnbnreuhdc 47 ordb bnctnod mdc 6; ordb tnluco tnrjou. Ynmdcohdc sntjdp hun frlwcjns bnbnreuhdc 46 ordb bnctnod mdc 9; ordb tnpuco tnrjou. Jfu `ncmdh bnbfudt enfj` mdrj 6 elydco hun edpjs enojt mdc snhurdco-hurdcocyd 4 elydco hun frlwcjns. Fudted` blmne bdtnbdtjhd mdrj bdsded` tnrsnfut.

 

 Edbpjrdc

[NCJEDJDC YJHD[

Ydtu Ydtudc dc [ncm [ncmjm jmjh jhdc dc

1 YBD YBD Cnon Cnonrj rj 4 Ije Ijedb dbdy dydd

Bdtd [nedadrdc

1 Bdtnbdtjhd

Hneds/Ynbnstnr

1 PJ /4

]d`uc pnedadrdc

1 6;6;/6;64

4. Vufr Vufrjh jh [ncje [ncjedj djdc dc Yjhd Yjhdp p 6.  Cl . 4

6

9

Jcmjhdtlr  Yjhdp ]dcoouco Adwdf

Ydcodt Fdjh (YF) Yumd` dbfje  fdojdc bncynensdjhdc tuods

Fdjh (F) Dmd usd`d dbfje  fdojdc bncynensdjhdc tuods

jcmjvjmu/hnelbplh  jcmjvjmu/hnelbpl tntdpj fneub h snidrd tnrushlcsjstnc bncnrus mdc hlcsjstnc ]nrejfdt dhtjg Hnradsdbd ]nrejfdt dhtjg  fnhnradsdbd  fnhnradsdbd mdedb hnojdtdc mdedb hnojdtdc hnelbplh snidrd hnelbplh cdbuc tnrus-bncnrus mdc  fneub hlcsjstnc hlcsjstnc Bncucauhhdc [nridyd Mjrj Ynedeu sjhdp pnridyd mjrj bncucauhhdc (fnrdcj mdedb prlsns sjhdp pnridyd mjrj  prnsnctdsj,  fnrtdcyd,  fnrpncmdpdt dtdu bncadwdf  pnrtdcyddc)

mdedb prlsns  pnbfnedadrdc snidrd tnrusbncnrus snidrd hlcsjstnc

 pnbfnedadrdc cdbuc fneub hlcsjstnc

Iuhup (I) Dmd snmjhjt usd`d dbfje fdojdc bncynensdjhdc tuods

Hurdco (H) ]jmdh dmd usd` dbfje fdojdc mdedb bncynensdjhdc

jcmjvjmu/hnelbplh  tuods jcmjvjmu/Hnelbplh  tntdpj fneub hlcsjstnc Dmd usd`d  fnhnradsdbd mdedb hnojdtdc hnelbplh cdbuc  fneub hlcsjstnc

]jmdh dmd usd`d  fnhnradsdbd mnedb hnojdtdc hnelbplh 

Dmd sjhdp pnridyd ]jmdh dmd sjhdp mjrj snedbd prlsns  pnridyd mjrj snedbd  prlsns  pnbfnedadrdc cdbuc tjmdh hlcsjstnc

 pnbfnedadrdc

 

9. En Enbf bfdr dr [ncje [ncjedj djdc dc Yjhdp Yjhdp  Cl.

Cdbd [nsnrtd Mjmjh ]dcoouco Adwdf YF F I H

Yjhdp Hnrad Ydbd YF F I H

[nridyd Mjrj YF F I H

 

 

 Edbpjrdc

[NCJEDJDC HN]NVDB[JEDC

Ydtu Ydtudc dc [ncm [ncmjm jmjh jhdc dc

1 YBD YBD Cnon Cnonrj rj 4 Ije Ijedb dbdy dydd

Bdtd [nedadrdc

1 Bdtnbdtjhd _dajf

Hneds/Ynbnstnr

1 PJ /4

]d`uc pnedadrdc

1 6;6;/6;64

Hlbpntncsj Md Mdsdr

1 Bncanedshdc prlordb ejcndr mud vdrjdfne mdc bntlmn

 

 Cl . 4.

pncynensdjdccyd

J[H

Bdtnrj

Jcmjhdtlr

Bnbprnsnctdsjhd

Blmne Mjfnrjhdc bdsded` bdtnbdtjhd hlctnhstude bnconcdj c pncynensdjdc  pdmd prlordb  prlordb ejcndr mncodc mud bdsded` ejcndr  gucosj hncmded fnrupd  pnrtjmdhsdbddc ejcndr mud hlctnhstude ydco vdrjdfne mncodc gucosj  fnrhdjtdc mncodc tuaudc fnrupd g(x,y) 2 dx+fy. [nsnrtd mjmjh mdpdt blmne bdtnbdtjhd bnbfudt blmne  pdmd prlordb bdtnbdtjhd mncodc fncdr.

]nhcjh   [ncjedjdc [rlsns

ejcndr mud vdrjdfne.

6.

Bncnctuhdc

 Cjedj

Mjfnrjhdc bdsded`

 pncynensdjdc bdsded` hlctnhstude ydco  fnrhdjtdc mncodc cjedj lptjbub mdrj  pnrbdsded`dc  prlordb ejcndr mud vdrjdfne mncodc bntlmn uaj tjtjh plalh.

lptjbub mncodc bncooucdhdc bntlmn uaj tjtjh plalh 

hlctnhstude bnconcdj  prlordb ejcndr mncodc mud gucosj hncmded fnrupd  pnrtjmdhsdbddc ejcndr mud vdrjdfne mncodc gucosj tuaudc fnrupd g(x,y) 2 dx+fy. [nsnrtd mjmjh mdpdt bncnctuhdc cjedj lptjbub bncooucdhdc bntlmn uaj tjtjh mncodc fncdr.

[rlsns

 

 Edbpjrdc ENBFDV [NCJEDJDC [NC^ODYDC

Ydtudc [ncmjmjhdc Bdtd [nedadrdc ]lpjh Hneds/Ynbnstnr

1 1 1 1

YBD Cnonrj 4 Ijedbdyd Bdtnbdtjhd [rlordb Ejcndr   PJ/Odcaje

]d`uc [nedadrdc _dhtu [ncjedjdc

1 1

6;6;/6;64 ´ 6 bjcoou sntned` tuods mjfnrjhdc

Hlbpntncsj Mdsdr 1 Vufrjh ]uods1

Bncidrj pnrbdsded`dc-pnrbdsded`dc ydco fnrhdjtdc mncodc bdtnrj [rlordb Ejcndr uctuh mjhnradhdc mdc mjidrj pncynensdjdccyd, mncodc dturdc1 4.

]uods mjhnradhdc mjhnradhdc snidrd snidrd fnrhnel fnrhnelbplh. bplh. Yndp hnelbpl hnelbplh h tnrmjrj tnrmjrj mdrj =-> =-> lrdco, lrdco, ydco ydco mjpje mjpjej` j` len` len` sjswd sncmjrj.

6. 9.

Fnrsdbd Fnrsdbd hnelbplh hnelbplh ydco mjpje mjpjej` j` len len` ` sjswd, sjswd, sjswd sjswd bncidrj bncidrj pnrbdsd pnrbdsded`dc ed`dc [rlord [rlordb b Ejcndr Ejcndr Yjswd Yjswd `d `drus rus mdpd mdpdtt bnci bncidrj drj bjcj bjcjbde bde 9 ancjs ancjs bdsd bdsded` ed` y ydco dco f fnrf nrfnmd nmd..

=.

Edplrdc Edplrdc `dsje `dsje prlynh prlynh tnrsnfut tnrsnfut mjhnh mjhnh mdc mj mjsusu susuc c bncadmj bncadmj snf snfud` ud` hejpjc hejpjco/bdhd o/bdhded` ed` sj sjcohdt cohdt mdc mdc mjajejm mncodc rdpj`.

>.

Fdtds Fdtds wdht wdhtu u pnco pnconrad nraddc dc tuods tuods ´ 6 bjcoou, bjcoou, mdc fdo fdojj sjswd sjswd ydco mdh mdh bncoubpu bncoubpuehd ehdc c tnpdt wdhtu, bdhd dmd sdchsj ydco dhdc mjfnrjhdc.

7.

Yn Yntne tned` d` tu tuod odss sn snen ensd sdjj mjhn mjhnra radh dhdc dc,, bd bdhd hd sj sjsw swd d mjwd mjwdaj ajfh fhdc dc uc uctu tuh h pr prnsn nsnct ctds dsjj mj mn mnpd pdc c hned hneds, s, bncydbpdjhdc `dsje tuods prlanhcyd.

Hrjtnrjd [ncjedjdc 1

4. 6. 9. =. >. 7. ?.

Hnsn Hnsnsu sudj djdc dc bdt bdtnr nrjj ydco ydco m mjt jtuo uods dshd hdc c Hntnpd Hntnpdtdc tdc pncy pncynen nensdj sdjdc dc mdtd mdtd mncod mncodc c idrd pncy pncydaj dajdcc dccyd yd Bnbudt Bnbudt sub subfnr fnr pnrl pnrlen` en`dc dc m mdtd dtd ydco ydco rnenvd rnenvdc c mdc vde vdejm jm Ed Edpl plrd rdc c mjh mjhnt ntjh jh md mdc c mja mjaje jejm jm rd rdpj pj Edplrdc Edplrdc mjhubpueh mjhubpuehdc dc tnpdt wdhtu snsudj snsudj mncodc mncodc hnsnp hnsnpdhdtd dhdtdc c Hnra Hnrads dsdb dbdd h hne nelb lbpl plh h ssdc dcod odtt fdj fdjh  h  [rns [rnsnc nctd tdsj sj hn hnel elbp bplh lh bnyd bnydhj hjch chdc dc

0. Hnbdbp Hnbdbpudc udc bncd bncdcoo coodpj dpj pnrt pnrtdcy dcyddc ddc mdrj mdrj hnel hnelbpl bplh h edjc edjc Yhlr/Cjedj Edplrdc 1 ; ’ 4;; , mjsnsudjhdc mdrj `dsje edplrdc mdc prnsnctdsj

 

Edbpjrdc- Enbfdr pncjedjdc plrtlglejl ENBFDV [NCJEDJDC [LV]LGLEJL

HM Ancjs ]uods Hneds Ynbnstnr/]d`uc[nedadrdc

 Cl

1 1 1 PJ 1 4/6;6;-6;64

Cdbd [nsnrtd Mjmjh/Hnelbplh Mjmjh/Hnelbplh

Cjedj

]dcmd ]dcodc [nsnrtd Ouru Mjmjh 

Hntnrdcodc (]oe [ncoubpuedc)

[nrubusdc Cjedj Dh`jr

   

A^BED@ YHLV  V^B^Y CJEDJ 2 \\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\ \ x 4;; 2 ......................... A^BED@ YHLV BDHYJBDE

[nmlbdc [ncshlrdc [lrtlglejl

Hrjtnrjd Yjswd bncyjbpdc snbud tuods ydco tned` mjhnradhdc mncodc encohdp, mdc tuods mjhnradhdc mncodc fncdr, snrtd mjhubpuehdc tnpdt wdhtu. Yjswd bncyjbpdc tuods-tuods ydco tned` mjhnradhdc, mdc snfdojdc fnsdr fncdr tdpj hurdco encohdp, snrtd mjhubpuehdc tnpdt wdhtu. Yjswd bncyjbpdc tuods-tuods ydco tned` mjhnradhdc, cdbuc snfdojdc fnsdr sded`, hurdco encohdp, mdc tjmdh mjhubpuehdc tnpdt wdhtu. Yjswd bncyjbpdc tuods-tuods ydco tned` mjhnradhdc, cdbuc tuods ydco mjhnradhdc sded`, mdc hurdco encohdp, snrtd tjmdh mjhubpuehdc tnpdt wdhtu. Yjswd tjmdh bncyjbpdc sdtu puc tuods-tuods ydco mjfnrjhdc hdrncd tjmdh pnrcd` bncoubpuehdc tuods.

Hntnrdcodc shlr 1 Bdsjco-bdsjco hlelb mjjsj mncodc hrjtnrjd Fdjh Ynhdej

Yhlr Bdhsjbde = 9 6 4 ;

 

Fdjh  Iuhup Hurdco  Cjedj 2

∔ shlr pnrlen`dc  ß 4;; shlr bdhsjbde bdhsjbde

Hrjtnrjd cjedj D 2 0; ’ 4;; 1 fdjh snhdej F 2 ?; ’ ?: 1 fdjh  I 2 7; ’ 7: 1 iuhup M 2 5 7; 1 hurdco

 

edbpjrdc  [ncjedjdc [rnsnctdsj 

Hneds 1 PJ Aubed  Cjedj ` shlr 

Dspnh [ncjedjdc  CL .

 CDBD

Hlb u cjhds j  

Yjstn

_dw

Hnfnr 

b dtjhd

d sdc

d cjdc

Onstur  dctusjd n mdc  pncdb s  pjedc

Hn t

 

 

 

Edbpjrdc ENBFDV LFYNVWDYJ [NCJEDJDC YJHD[ JCY]V^BNC [NCJEDJDC YJHD[

Yjhdp mdc pnrjedhu ydco mjdbdtj  CL.

CDBD

]nejt j E/[

H nntt 1 YF 2 Ydcodt Fdjh

F 2 Fdjh

I 2 Iuhup

H 2 hurdco

Ylpdc

Mjspejc

Auau r 

 

 

 

]doouco Dhtjg  Adwdf  

 

 

HVJ]NVJD [NCJEDJDC

4.

6.

9.

=.

>.

7.

]NEJ]J YF

2 Ajhd tjmdh pnrcd` hnejru

F

2 Ajhd pnrcd` hnejru (4-6)

I

2 Ajhd pnrcd` hnejru (9->)

H

2 Ajhd pnrcd` hnejru enfj` mdrj >

YL[DC YF

2 Ajhd tjmdh pnrcd` fnrhdtd furuh 

F

2 Ajhd pnrcd` fnrhdtd furuh (4-6)

I

2 Ajhd pnrcd` fnrhdtd furuh (9->)

H

2 Ajhd pn pnrcd` fnrhdtd fu furuh enfj` mdrj >

MJYJ[EJC YF

2 Ajhd tjmdh pnrcd` tnedt

F

2 Ajhd pnrcd` tnedt (4-6)

I

2 Ajhd pnrcd` tnedt (9->)

H

2 Ajhd pnrcd` tnedt enfj` mdrj >

A^A^V   YF

2 Ajhd uedcodc mncodc hnbdbpudc sncmjrj

F

2 Ajhd tn tnrej`dt iurdco edeu mjjcodthdc admj auaur 

I

2 Aj Ajhd tn tnrej`dt iu iurdco ed edeu mjjcodthdc ttnntdp au auaur 

H

2 Ajhd tnrdco-tnrdcodc iurdco

DH]JG YF

2 Ajhd dhtjg enfj` mdrj hndhtjgdc pdmd ububcyd

F

2 Ajhd dhtjg sdbd mncodc hndhtjgdc pdmd ubu bub bcyd

I H

2 Ajh Ajhdd pnr pnrc cd` dht dhtjg tdpj dpj hu hurd rdco co mdr mdrj h hnd ndht htjg jgdc dc pdm pdmd u ubu bubc bcyd yd 2 Ajhd tjmdh pnrcd` dhtjg  

]DCOO^CO AD_DF YF

2 Ajhd tuods fdous mdc tnpdt wdhtu

F

2 Aj Ajhd hd tu tuod odss fdou fdouss tdpj tdpj tn tned edt/ t/ Ajhd Ajhd tu tuod odss od odh h fdou fdouss tdpj tdpj tn tnpd pdtt wd wdht htu u

I

2 Ajhd tuods odh fdous mdc tnedt

H

2 Ajhd tjmdh bnconradhdc tuods

 

Bncontd`uj, Hnpded Ynhled`

 

Hdrdwdco, Ynptnbfnr 6;6; Ouru Bdtd [nedadrdc,

Mrs. @. ^mj` Ydbsumjc, B.B.[m

Jrvdc Cdabue Butdqjc, B.[m

CJ[. 4:7>;64?4:00;94;;?

CJ[. 4::;;4466;4:;94;;: