Page 71 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math2-2 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ lhek o lrrrk

• ;fn fdlh iQyu dh :
ij nf{k.k i{k rFkk oke i{k nksuksa lhek,¡ fo|eku rFkk ,dleku gksa] uksV
rks iQyu dh :
ij lhek dk vfLrRo gksrk gSA
f
x
lim ( ) : lim ( )f x : ! (ekuyks)
x → a + x → a −
• ;gk¡ ! iQyu dh lhek dgykrh gS rFkk bls ge fuEu izdkj ls O;Dr djrs gSaµ
f
lim ( ) : !
x
x → a
• gesa lhek Kkr djus osQ fy, nf{k.k i{k o oke i{k nksuksa lhek,¡ Kkr djuh pkfg, ijUrq ekè;fed Lrj
ij ge lhek vf/dka'kr% lh/s gh Kkr djrs gSaA
• va'k vkSj gj nksuksa dks mlosQ mHk;fu"B xq.ku[k.M tks 'kwU; ugha] ls Hkkx nsuk rqjUr lEHko u gks rks Js.kh
izlkj !"

;k fdlh :ikUrj.k
,
osQ ckn ;g fØ;k laHko gks
ldrh gSA
• ;fn fdlh iQyu dk ys[kkfp=k * "/ [khpus ij tks oØ izkIr gksrk gSA og bl izdkj gks fd
fdlh fcUnq :
ij VwVrk B u gks] (Hkax u gksrk gks) rks iQyu ml fcUnq ij lrr

dgykrk gSA
• 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 :
lim :
b
a
x →+ 0 x →− 0
2-16 'kCndks'k # )

• vuqØe 0 @
µØe] flyflykA

• lrr 7

( µyxkrkjA

2-17 vH;kl&iz'u )

 x − 2 2ax + a  2
lim  
1- x → 0  x − a  dk eku Kkr djsaA (mÙkj % )

a x − b x a
2- fl¼ djsa fd lim = log e .
x →0 x b
x − 1
3
lim
3- x→ 1 x − 1 dk eku Kkr djsaA (mÙkj % ))
 1 , x ≠0


4- iQyu : x osQ lkarR; dk ijh{k.k djsaA (mÙkj% vlarr)
 3 , x = 0

5- n'kkZ,¡ fd : 1 1 : - ij larr gSA