Page 59 - 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

bdkbZ lhek o lrrrk

2-14 larr iQyuksa ij izes; /$ "
3

uksV

;fn vkSj nksuksa fdlh fcUnq :
ij larr gksa rks ± Hkh :
ij larr
gksxkA

;fn vkSj nksuksa fdlh fcUnq :
ij larr gSa rks Hkh
:
ij larr gksxkA
;fn fdlh fcUnq :
ij larr gS vkSj ,d fuf'pr okLrfod la[;k gS rks Hkh
:
ij larr gksxkA
f ()
x
;fn vkSj fdlh fcUnq :
ij larr gS vkSj
≠ 0 rks Hkh :
ij larr
g () x
gksxkA
1
;fn 9 :
ij larr gS vkSj 5
≠ 0 rks Hkh :
ij larr gksxkA
f () x
;fn 9 :
ij larr gS rks 1 P Hkh :
ij larr gksxkA

mnkgj.k 1- fn[kkb, fd iQyu

# ij larr gSA
gy % lim : :
x → 2

vr% iQyu : ij larr gSA
1
mnkgj.k 2- iQyu

# ij vlarr gSA fl¼ dhft,A
x − 2

gy % ifjHkkf"kr ugha gS (gj 'kwU; gS)A
Y
lim dk vfLrRo ugha gS (∞ osQ cjkcj gS)A
x → 2
: dks NksM+dj vU; izR;sd fcUnq ij iQyu larr gSA vr% :
O
ij iQyu vlkarR;

( gSA 2 X

x 2 − 4
mnkgj.k 3- fn[kkb, fd iQyu

# ij vlarr
x − 2

gSA Y
4
gy % ifjHkkf"kr ugha gS (va'k vkSj gj nksuksa 'kwU; gSa)A
lim :
x → 2

vr% iQyu : vlarr gSA
O 2 X
mnkgj.k 3 esa vlkarR; dks nwj fd;k tk ldrk gS D;ksafd iQyu dks iqu%
2
x − 4
: 9 ≠ H ifjHkkf"kr djosQ :
x − 2