Page 29 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

fJekJh^1 L cbB

wzfBnk fe wzr cbB, q = 16 – 4p j? HHHH(i) B'N
ns/ g{osh cbB, q = –8 + 4p j? HHH(ii)

fiZE/, q t;s{ dh wksok ns/ p t;s{ dh ehws do;kT[Ad/ jB.
j[D n;hA q ns/ p dk nfijk wkB eZYD dk :sB eoKr/ fijVk ;wheoD (i) ns/ (ii) d'B'A B{z
;zs[PD eoB. fJ;d/ bJh d'B'A ;wheoDK B{z jZb eoBk j't/rk. wzr ns/ g{osh dh ;kw:kt;Ek
ftZu

p dk wkB ;wheoD (i) ftZu oZyD s/
q = 16 – (4 × 3) = 16 – 12 = 4
fJ; soQK ;kw:kt;Ek ehws & 3 ns/ wzr ns/
g{osh dh wksok 4 fJekJhnK ftZu j't/rh.
fJjBK ;wheoDK B{z n;hA o/ykfuZso d/ o{g ftZu
th gqdofPs eo ;ed/ jK.
o/ykfuZso ftZu X-neP T[Zs/ t;s{ dh wksok
ns/ Y-neP T[Zs/ t;s{ dh ehws do;kJh rJh
j?. DD wzr cbB ns/ SS g{osh cbB B{z
do;kT[Ad/ jB. d'B'A cbB fJZe^d{i/ B{z E fpzd{
T[Zs/ eZNd/ jB. fJ; soQK ;kw:kt;Ek th E
fpzd{ T[Zs/ jh gqkgs j't/rh. fJ; fpzd{ T[Zs/ Y –
G{iKe ;kw:kt;Ek w[Zb ns/ X-G{iKe wzr ns/
g{osh wksok dZ;/rk.
fJ; soQK ;kw:kt;Ek w[Zb & 3 ns/ t;s{ dh
wksok & 4 j't/rh.
noEPk;so ftZu gq:'r j'D tkb/ cbB
(T) gotb (Parobola) (n) nfsgotb (Hyperbola)
(J) bx[rDe cbB (Logarithmic Function) ns/
(;) xksh cbB (Exponential Function).

(T) gotb (Parobola)L gotb dk noEPk;so ftZu pj[s T[g:'r j[zdk j?. i/eo y, x ns/ T[;dh
d{ih xks s/ fBoGo eodk j't/ sK y B{z x dk d'xksh (quardratic) cbB efjzd/ jB. fJ;B{z j/m
nB[;ko do;kfJnk ik ;edk j?^
2
y = a + bx + cx ...(i)
fJ;h soQK x, y ns/ T[;dh d{ih xks T[Zs/ fBoGo eodk j't/ sK x B{z y dk d'xksh cbB efjzd/ jB.
fJ;B{z rfDs o{g ftZu j/m nB[;ko do;k ;ed/ jB^
2
x = a + bx + cy ...(ii)
T[go'es (i) ns/ (ii) gotb d/ ;XkoD cbBh o{g B{z do;kT[Ad/ jB. fJZE/ fJj T[b/y:'r j? fe
2
2
gobt d/ ;wheoD ftZu (i) xy dk gd BjhA j[zdk j? ns/ (ii) x iK y ftZu fJZe jh j[zdk j?.
fJZE/ fXnkB d/D :'r rZb fJj j? fe T[go'es ;wheoD dk e/Ado w[Zb fpzd{ T[Zs/ BjhA j't/rk fit/A fe
o/ykfuZso ftZu do;kfJnk frnk j?^

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