Page 46 - 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 1  1 
lim - ; , : lim ,
- 8 , : 8 ,
− 

h→ 0 h→ 0 h  h 
1  1 
: lim , G lim
lim - 8 , : lim 8,
−
h→ 0 h→ 0 h h→ 0 h→ 0   h  
: - <8 rFkk 1 osQ eè; fLFkr lim  1 

,d ifjfer
jkf'k= : h→ 0 8, lim
− h  
h→

0
;k - ; - : - :8- <8 rFkk 1 osQ eè; fLFkr ,d
1 ifjfer
jkf'k=
8 , : 8 ,
x − h
;k - 8 - : -

2-4 lhek dk vfLrRo

( "

;fn fdlh iQyu dh :
ij nf{k.k i{k rFkk oke i{k nksuksa lhek,¡ fo|eku rFkk ,dleku gksa] rks iQyu
dh :
ij lhek dk vfLrRo gksrk gSA
f
x
vFkkZr~ lim ( ) : lim ( )f x : ! (eku yks)
x → a + x → a −
;gk¡ ! iQyu dh lhek dgykrh gS rFkk bls ge fuEu izdkj ls O;Dr djrs gSaµ
f
x
lim ( ) : !
x → a
2-5 iQyu dh - ij lhek rFkk eku esa vUrj

. )
( "

x
f
lim ( )
x a
1- iQyu dh lhek og jkf'k gS ftldh vksj iQyu og jkf'k gS tks fd iQyu esa j[kus ij izkIr
Øe'k% vxzlj gksrk gS tc Lora=k pj dk eku dh tkrh gSA
dh vksj gksrk gSA
2- lhek Kkr djus osQ fy, gesa osQ fudVorhZ ij eku fudkyus osQ fy, osQoy ij
osQ ekuksa dk vè;;u djuk iM+rk gS rFkk dk eku fudkyuk iM+rk gSA
fu"d"kZ fudkyuk iM+rk gSA

3- ij iQyu dh lhek dk vfLrRo gks ldrk ij iQyu dk eku ugha Hkh gks ldrkA
gSA
2-6 iQyu dk eku vkSj lhek
( "

pj osQ fdlh eku
osQ fy, iQyu dk eku vkSj lhekar eku fHkUu gksuk vko';d ugha gSA oqQN bl
izdkj osQ iQyu Hkh gksrs gSa ftuosQ fy, :
ij dk eku rFkk lhekar eku cjkcj gksrs gSa vFkkZr~

: lim ( )f x
x → a