Page 57 - 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

2-10 fdlh fcUnq ij iQyu dk lkarR; uksV
3

dkW'kh ifjHkk"kk / 6 2 % ,d iQyu
ij larr dgykrk gSA ;fn ,d
LosPN pquh xbZ /ukRed la[;k tks fdruh Hkh NksVh gks fdUrq 'kwU; u gks] osQ fy, ge
ij fuHkZj ,d ,slh /ukRed la[;k
,slh izkIr dj losQ fd * * . osQ mu lHkh
ekuksa osQ fy, ftuosQ fy,
% . * * .
"

vFkkZr~ vUrjky
8 δ9
; δ osQ fdlh Hkh fcUnq ij iQyu rFkk
dk /ukRed vUrj ,d
LosPNr;k fufnZ"V /ukRed la[;k ε ls Hkh de gks] rks iQyu fcUnq :
ij larr dgykrk gSA

oSdfYid ifjHkk"kk% iQyu 9 :
ij larr 7

dgykrk gS ;fn lim dk vfLrRo gks
x → a
vkSj og :
ij iQyu osQ eku osQ cjkcj gksA

uksV~l lim :
vFkkZr~ < dh lhek] tc →
= : <iQyu dk eku] tc :
=
x → a
vr% ;fn
; - :
8 - :
9 rks dks :
ij larr dgrs gSaA vU;Fkk :
ij iQyu vlarr
gSA iQyu fcUnq :
ij larr dgykrk gS ;fn iQyu fuEufyf[kr rhu 'krks± dh iqf"V djs %

1- ;fn iQyu 9 :
ij ifjHkkf"kr gks vFkkZr~ :
ij iQyu dk ,d fuf'pr eku gksA
2- tc dk eku
dh vksj vxzlj gks] rc fdlh lhek dh vksj vxzlj gks vFkkZr~ lim dk vfLrRo

x → a
gksA

3- lim :
gksA
x → a

2-11 lkarR; dk T;kferh; vFkZ & "

! 3

eku yks ( iQyu dk ys[kkfp=k gSA bl ys[kkfp=k esa fcUnq '<
9
= ij fopkj djksA ;fn ε dksbZ LosPNr;k
fufnZ"V /ukRed la[;k gS rks js[kk,¡ :
8ε9 :
F H
; ε9 $v{k osQ lekUrj vkSj ' osQ uhps dh vksj rFkk mQij Y
dh vksj gksxhA
Q
fn;s gq, ε osQ laxr :
osQ ifjr% ge ,d vUrjky
C D
ftldh pkSM+kbZ δ gS] Kkr dj ldrs gSa ftls js[kk :
y =(
f x)
osQ nksuksa vksj rFkk Av{k osQ lekUrj js[kkvksa :
δ fa()
P
vkSj :
δ }kjk iznf'kZr fd;k tk ldrk gSA
A B
;fn nks js[kkvksa :
8 δ9 :
; δ osQ chp iQyu
osQ ys[kkfp=k dk izR;sd fcUnq nks js[kkvksa :
R X
O
a
x =
E G