Page 56 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math2-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV

K

a a a
i ii iii
() () ()
blosQ foijhr ;fn fdlh fcUnq :
ij iQyu dk ys[kkfp=k VwV B tk, rks fcUnq :
ij iQyu
vlrr

dgyk;sxkA iQyuksa osQ fuEu ys[kkfp=kksa dks ns[kdj Kkr gksrk gS fd fp=k
esa osQ ys[kkfp=k esa fcUnq :
ij fdlh mQ¡pkbZ mnkgj.kkFkZ dk ,d ^mNky* ," gS fd ;fn ge
ys[kkfp=k osQ vuqfn'k ck;ha vksj ls nk;ha vksj py jgs gksa rks :
,d Hkax B gS vkSj gesa :
dh
,d vksj ls nwljh vksj pyus esa iasfly dks mBkuk iM+sxkA iQyu dk oØ Hkh :
ij Hkax B gSA
iQyu :
ij Hkax B ugha gS vFkkZr~ oØ bl izdkj gS fd VwVrk ugha gSA vr% iQyu
9 :
ij larr gSA

mnkgj.k ;fn ge iQyu : dk ys[kkfp=k [khaps rks ;g ,d Y
ijoy; gksrk gS tSlk fd vkÑfr esa fn[kk;k x;k gSA ,sls iQyuksa osQ
ys[kkfp=k ij ;fn ge nkfgus ls ck;sa ;k ck;sa ls nkfgus ,d rjiQ ls
nwljh rjiQ pysa rks ge dksbZ Øe&Hkax ugha ik;saxs vkSj ;fn ge
ys[kkfp=k ij ,d fdukjs ls nwljs fdukjs ij isafly pyk;sa rks chp esa y
dgha Hkh iasfly mBkuh ugha iM+sxhA ;g iQyu larr iQyu 7
x

gSA X O X
 1 2
 2 x x <1 Y
 
mnkgj.k : 1  x 1
 1
1  x, x > 1
2
  2
dk ys[kkfp=k ;fn ge [khaps rks nks fofHkUu ijoy; rFkk ,d fcUnq (1] 1) izkIr gksxk tSlk fd vkÑfr esa fn[kk;k
x;k gSA ;gk¡ ;fn ge nkfgus ls ck;sa ;k ck;sa ls nkfgus pysa rks] :
ij Øe Hkax gS vkSj ;fn ge : osQ ,d rjiQ ls nwljh rjiQ
isafly pyk;sa rks : ij isafly dks mBkuk iM+sxkA ;g
2
iQyu vlarr

gSA
ge ns[krs gSa fd ;fn fdlh fcUnq ij iQyu vlarr gS rks ml fcUnq
1
ij iQyu osQ eku esa ,dk,d Nykax

," gksrh gS
tcfd larr iQyu dk eku] dk eku cnyus ij /hjs&/hjs cnyrk
gSA vr% ;fn fdlh fcUnq :
ij iQyu larr gS rks P 8 2 1 1 2

P dk eku] dks
osQ cgqr lfUudV pqudj LosPNkuqlkj NksVk fd;k tk ldrk gSA