Page 58 - 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 8 ε9 :
; ε osQ chp esa Hkh gks rks iQyu fcUnq :
ij larr gSA

mnkgj.kr % vpj iQyu

: 9 osQ izR;sd okLrfod eku osQ fy, larr gSA
iQyu :

rFkk :
osQ izR;sd okLrfod eku osQ fy, larr gSA

2-12 fdlh fcUnq ij iQyu dk lkarR; Kkr djus dh fof/ $

!
3

4

lhek , dh ifjHkk"kk ls Li"V gS fd lim dk vfLrRo !

rHkh gksrk gS] tc
x → a
dh oke i{k lhek
dh nf{k.k i{k lhek

vFkkZr~ lim : lim
x → a − x → a +
vFkok
8 - :
; -
vr% fcUnq
ij iQyu dk lkarR; iznf'kZr djus osQ fy, gesa fn[kkuk pkfg,
fd bl fcUnq ij dh oke i{k lhek
dh nf{k.k i{k lhek
iQyu dk eku
1 2 0 1
/ 0 1
7 ! 2 / 2

vFkkZr~ lim : lim
+
−
x → a x → a
vFkok
8 - :
; - :
nf{k.k i{k lhek O 3 osQ fy, esa :
; , j[kks] tgk¡ , → -9 tc →
oke i{k lhek 3 O 3 osQ fy, esa :
8 , j[kks] tgk¡ , → -9 tc →

2-13 ,d vUrjky esa iQyu dk lkarR;
3

,d iQyu fdlh foo`r vUrjky
9 esa larr dgk tkrk gS ;fn ;g vUrjky
9 esa osQ lHkh ekuksa
osQ fy, larr gSA
iQyu fdlh lao`r vUrjky

<
9 = esa larr dgk tkrk gS] ;fn
;g osQ mu lHkh ekuksa osQ fy, larr gks ftlosQ fy,
L L

lim :
a
x →+ 0
lim :
x →− 0
b
vFkkZr~ iQyu [kqys vUrjky
9 esa larr gks rFkk :
ij nf{k.k i{k ls rFkk : ij oke i{k ls larr
gksA
,d vUrjky esa vlkarR;

(

% iQyu fdlh vUrjky esa vlarr dgk
tkrk gS ;fn ;g vUrjky esa fdlh ,d fcUnq ij vFkok cgqr ls fcUnqvksa ij vlarr gksA