Page 136 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math7-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV 7-4-2 lh-bZ-,l- mRiknu iQyu dk dkWc&MksXyl mRiknu iQyu ij ykHk
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1- lh- bZ- ,l- / 4 mRiknu iQyu dkWc&MksXyl mRiknu iQyu dkWc&MksXyl mRiknu iQyu dh vis{kk
vf/d lkekU; mRiknu rduhdh iznf'kZr djrk gSA lh-bZ-,l- mRiknu iQyu esa izfrLFkkiu yksp fLFkj gksrh gS
rFkk rFkk vko';d ugha gS fd ;g yksp bdkbZ osQ cjkcj gksA
2- lh- bZ- ,l- mRiknu iQyu dkWc&MksXyl mRiknu iQyu dh vis{kk vf/d egÙoiw.kZ iSjkehVlZ 1 7

j[krk gSA bl izdkj bldk izfrLFkkfirrk
. rFkk oqQ'kyrk esa vf/d foLr`r {ks=k
gSA
3- dkWc&MksXyl iQyu lh-bZ-,l- mRiknu iQyu dk gh ,d fo'ks"k :i gksrk gSA ;fn lh-bZ-,l- iQyu α ( +
esa j[k nsa rks dkWc&MksXyl iQyu izkIr gks tk;sxkA
4- lh-bZ-,l- mRiknu iQyu osQ iSjkehVlZ dk vuqeku yxkuk vklku gksrk gSA blosQ vfrfjDr bl iQyu us
dkWc&MksXyl iQyu dh lHkh leL;kvksa rFkk vokLrfod ekU;rkvksa dks nwj dj fn;k gSA

7-4-3 lh-bZ-,l- mRiknu iQyu dh lhek;sa $
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;|fi lh-bZ-,l- mRiknu iQyu us dkWc&MksXyl iQyu dh lHkh leL;kvksa rFkk vokLrfod ekU;rkvksa dks nwj
dj fn;k gS vkSj vFkZ'kkL=k esa Hkh bldk {ks=k O;kid gS] fdUrq fiQj Hkh bldh fuEu vkykspuk;sa dh tkrh gSaµ

1- lh-bZ-,l- mRiknu iQyu Hkh dkWc&MksXyl dh Hkk¡fr mRifÙk osQ osQoy nks lk/uksa (Je rFkk iw¡th) dks ysdj
pyrk gSA ;g mRifÙk osQ vf/d lk/uksa osQ fy;s ykxw ugha gksrk gSA izks-,p-mtkok 1 2 >H # dk
dguk gS fd bl iQyu dks &mRifÙk osQ lk/uksa osQ fy;s ykxw djuk dfBu gSA

mnkgj.kµ;fn ( A ab mRiknu iQyu gS] rFkk lk/u osQ fy, ek¡x Kkr dhft;s tcfd mudh dhersa
rFkk fLFkj gSaA ;fn ek¡x oØ ( β * α gksa rks lk/u dh ek¡x dherksas rFkk fLFkjkad esa D;k gksxh\

( A ab

)

E 5
E 5 #

( β * #

gy
µfn;k gqvk mRiknu iQyu
( A ab
( $

lehdj.k
dks i`Fko~Q&i`Fko~Q :i esa E 5 rFkk E 5 osQ lUnHkZ esa vodyu djus ij
∂x ( 1 Aa −1/ 2 1/ 2
b
∂a 2

∂x 1 1/ 2 −1/ 2
rFkk ( Aa b
∂b 2