Page 48 - 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 tc iQyu dh lhek Lora=k pj osQ eku osQ ck;ha vksj ls izkIr dh tkrh gS rks mls --------- dgrs gSaA

;fn fdlh iQyu dh :
ij nf{k.k rFkk oke i{k nksuksa lhek,¡ fo|eku rFkk ,dleku gksa] rks
---------
iQyu dh :
ij lhek dk gksrk gSA
pj osQ fdlh eku
osQ fy, iQyu dk eku vkSj --------- eku fHkUu gksuk vko';d ugha gSA
---------
;|fi gesa lhek Kkr djus osQ fy, nf{k.k i{k o oke i{k nksuksa lhek,¡ Kkr djuh pkfg, ijUrq Lrj
ij ge lhek vf/dka'kr% lh/s gh Kkr djrs gSaA

gy lfgr mnkgj.k

dHkh&dHkh mHk;fu"B xq.ku[k.M ls Hkkx nsuk ljy ugha gksrk gSA ,slh fLFkfr esa fof/ dk mi;ksx djosQ
lhek lqxerk ls tkuh tk ldrh gSA fuEu mnkgj.kksa ls fØ;k Li"V gks tk;sxhA
fVIi.khµva'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
x 3 − a 3
mnkgj.k 1- lim dk eku Kkr dhft,A
x → a x − a

x − a 3 (x − ax + ) ( 2 a + 2 ax )
3
gy % lim : lim
x → a x − a x → a (x − ) a

: lim ;
;
9 < ≠
=
x → a

:
;
;
:
mÙkj
x
log (1 + ) − x
mnkgj.k 2- lim e dk eku fudkfy,A
x 0 x 2
 x − x 2 + x 3 − ... −  x
log (+ x) − x   2 3  
1
gy % lim e : lim
x → 0 x 2 x → 0 x 2
x 2 x 3 2  1 x 
− + − ... x  − + − ... 
: lim 2 3 : lim  2 3 
x → 0 x 2 x → 0 x 2
 1 x 
: lim −  + − ... 
x → 0  2 3 
1 1
−
: − + 0... : − mÙkj
2 2

x 3 − b 3
lim

VkLd dk eku fudkysaA 4mÙkj% ) 5
x → b x − b