Page 70 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math2-2 IInd 6-8-11 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  x
lim 1 +  :

x→∞  x 
1

8
∞
e

x
a − b x
e
lim = log ....
x → 0 x
b 1 a a

−
a b b b

;fn vkSj nksuksa fdlh fcUnq :
ij larr gksa rks N 9 :
ij D;k gksxk\

larr vlarr laxr
vlaxr

e x 2 − 1
lim e x 2 + 1 = ......
x→∞

1

e

2-15 lkjka'k % ""

• tc iQyu dh lhek Lora=k pj osQ eku osQ nkfguh vksj ls izkIr dh tkrh gS rks mls iQyu dh nf{k.k
i{k lhek "0"1" dgrs gSa vkSj nkfguh vksj osQ fy, /u fpÉ dk iz;ksx djrs gq, lkaosQfrd :i
eas fuEu izdkj ls fy[krs gSaµ
nf{k.k i{k lhek :
; -

: lim ( )f x : !
x → a +

• tc iQyu dh lhek Lora=k pj osQ eku osQ ck;ha vksj ls izkIr dh tkrh gS rks mls oke i{kh; lhek
dgrs gSa vkSj ck;ha vksj osQ fy, 8 fpÉ dk iz;ksx djrs gq, lkaosQfrd :i esa fuEu izdkj ls fy[krs
gSaµ

oke i{k lhek :
8 -
: lim ( )f x : !
x → a −
• nf{k.k i{k rFkk oke i{k lhek Kkr djus osQ fy, iQyu esa pj osQ LFkku ij Øe'k% ; , rFkk
8 , izfrLFkkfir dhft,A
• bl izdkj ls izkIr iQyu dks fn;s gq, fcUnq (eku yks
) ls izfrLFkkfir dhft,A
• , → - ij iQyu dh lhek Kkr dhft, <vFkkZr~ ls izkIr iQyu dks mi;qZDr :i esa j[kdj , :

- jf[k;s=A