Page 76 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math3-1 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 Kkr djus dh bl fozQ;k dks vodyu djuk dgrs gSa ;k fdlh iQyu osQ vody&xq.kkad Kkr djus dh lafozQ;k
dks vodyu

dgrs gSaA

dy y δ
D;k vki tkurs gSa : lim
dx x δ→ 0 x δ
y δ dy y δ
fo|kfFkZ;ksa dks rFkk osQ vUrj dks cM+h lko/kuh ls le>uk pkfg,A ,d fHkUu gS ftlosQ va'k
x δ dx x δ
dy y δ
vkSj gj dks ,d&nwljs ls vyx fd;k tk ldrk gS fdUrq fHkUu ugha gS vfirq fHkUu osQ lhekar eku
dx x δ
,
* dks izdV djus dk ,d laosQr ek=k gSA
dks
ls vyx ugha fd;k tk ldrkA bldks
dy

cVs

"

i<+uk v'kq¼ gSA dks Mh Mh ,Dl vkWiQ okbZ <

= i<+k tkrk gS vkSj
dx
d
tSls ge igys crk pqosQ gSa bldk vFkZ gS vFkkZr~ dk osQ lkis{k vody&xq.kkadA
dx

3-2 ifjHkk"kk

x
;fn dk dksbZ iQyu vkSj
dk ogh iQyu
gks rks lim ( + f x ) − x f ( )
x → 0 x

dk lhekUr eku ! 8 ! osQ lkis{k dk vody&xq.kkad ;k vodyu 22 9
! 22 dgykrk gSA
dy df () d
x
fVIi.kh 1- lk/kj.kr% vody&xq.kkad

dks 9 ′9 9 , 9

dx dx dx
′ 9 ′ bR;kfn laosQrksa ls izdV djrs gSaA
fVIi.kh 2- fdlh iQyu osQ vody&xq.kkad

dks Kkr djus dh fof/ dks iQyu
dk vodyu djuk

* /

dgrs gSaA
vr% ge ns[krs gSa fd vodyu dh fof/ esa pkj in
"
gksrs gSa%
izFke inµ dks ; δ esa cnyuk rFkk ; δ Kkr djukA

f}rh; inµvUrj ; δ 8 Kkr djukA
x
( f x +δ ) x − f ( )
r`rh; inµvUrj dks δ ls foHkkftr djuk vkSj bl izdkj Kkr djukA
δ x
x
( f x +δ ) x − f ( )
prqFkZ inµtc δ 'kwU; dh vksj vxzLr gksrk gS rc vuqikr dh lhek Kkr djukA
x δ
fVIi.khµ;gk¡ ls vkxs dh o`f¼ δ osQ LFkku ij , fy[kk tk;sxk rkfd fo|kFkhZ δ vkSj dh nqfo/k esa u iM+saA
blfy, ;fn 9 dk dksbZ iQyu gS rks