Page 359 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math24-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ vkxr&fuxZr fo'ys"k.k

n + 1 uksV
4 ∑ aX P
vFkok ij i i
j = 1
n + 1
4 ∑ aX P
vFkok ij i i 4 / " (
j = 1
4 7 7
lehdj.k (24-7) larqyu lehdj.kksa dk f}rh; leqPp; gSA

24-4-1 fy;ksfUViQ osQ izkoSfxd fun'kZ ij laf{kIr fVIi.kh

LFkSfrd fun'kZ esa vFkZO;oLFkk osQ fofHkUu {ks=kksa osQ rduhdh xq.kkadksa dh lgk;rk ls ikjLifjd fuHkZjrk dk
vè;;u djrs gSaA fdUrq ;s xq.kkad vFkZO;oLFkk esa LVkWd : dh okLrfod vko';drk ij izdk'k ugha
Mkyrs gSaA ;s ;g Hkh crkus esa vleFkZ jgrs gSa fd lk/u dh og ek=kk tks fd m|ksx }kjk [kir dh tkrh gS]
osQ fy, fdruh iw¡th dh vko';drk gksxhA bl iw¡th dh ek¡x fLFkj iw¡th fofu;ksx tSls fuekZ.k] e'khu bR;kfn
vFkok mRiknu osQ fy, dPps eky dk LVkWd cuk;s j[kus osQ fy, dh tkrh gSA ;fn fLFkjkRed vkxr&fuxZr
fun'kZ ([kqyk fun'kZ) osQ varxZr iw¡th dk izHkko lfEefyr dj fy;k tk,] rc ;g O;oLFkk xR;kRed gks tkrh
gSA vr% iw¡th fuos'k bl xR;kRed vkxr&fuxZr fun'kZ dk ,d vfHkuo y{k.k gSA
bl izdkj vkxr&fuxZr LFkSfrd fun'kZ ([kqyk fun'kZ) esa ftu lajpukRed lehdj.kksa dk lgkjk fy;k tkrk gS]
mlesa izR;sd {ks=k osQ fy, vko';d iw¡th le; vUrjky lfgr lfEefyr dj fy;k tkrk gSA vr% ;g fun'kZ
LFkSfrd vkxr&fuxZr fun'kZ (fy;ksfUViQ [kqyk fun'kZ) dk foLrkj ek=k gSA
ekU;rk,¡ (

vkxr&fuxZr xR;kRed fun'kZ LFkSfrd fun'kZ dk lkekU;Ñr :i gSA vr% bldh ekU;rk,¡ LFkSfrd fun'kZ osQ
vuq:i gksaxhA tSlsµ(1) izR;sd m|ksx osQoy ,d gh le:i oLrq dk mRiknu djrk gS rFkk (2) izR;sd oLrq
osQ mRiknu osQ fy, osQoy ,d gh rduhdh miyC/ gS] tgk¡ mRifÙk osQ lk/uksa dk la;ksx fLFkj gSA
ekuk
pkyw o"kZ dk miHkksx gS tks osa m|ksx }kjk mRikfnr gksrk gSA osa m|ksx dk le; vof/ esa

oqQy mRiknu gS tks rhu mís';ksa osQ :i esa dke esa vkrk gSµ vxyh vof/ osQ miHkksx A
3 B7

m|ksxksa esa iw¡th oLrqvksa dk fo'kq¼ LVkWd ! 3 5 ! rFkk vFkZO;oLFkk esa vkS|ksfxd mRiknu

dk pkyw izokgA bu fLFkfr;ksa esa larqyu lehdj.k gksxkµ
4
3 3 ! 3 5 ! 3 3

(;gk¡ 4 7 )
vc loky ;g mBrk gS fd pkyw mRiknu rFkk oSQls mRiknu gksrk gS\ fy;ksfUViQ mRiknu iQyu

esa oqQy mRiknu nks izdkj osQ lk/uksa dk iQyu gksxkµ pkyw o"kZ osQ fy, dPpk eky rFkk iw¡thxr oLrqvksa
dk LVkWdµ
4 < 7 7 ! 7 ! =

4 < 7 7 ! 7 ! =

vFkZO;oLFkk esa oqQy iw¡th LVkWd lHkh m|ksxksa osQ iw¡th LVkWd dk ;ksx gksxkµ
! 4 ! 3 !