Page 64 - 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 O 3 : lim f ( ) : lim (0f + ) h
x
x → 0 + 0 h → 0
|0 − h | h
: lim : lim :
h → 0 0 + h h → 0 h
∴ O 3 ≠ 3 O 3

vr% iQyu : - ij vlarr gSA
3 O 3 : O 3 :

vr% : ij iQyu larr gSA mÙkj
 3ax , b x 1

mnkgj.k 8- ;fn
 11 , x 1
 5ax − 2b , x 1


ij ,d larr iQyu gS] rks vkSj osQ eku Kkr dhft,A
gy % pw¡fd fn;k gqvk iQyu 9 : ij larr iQyu gSA vr%
x
f
lim ( ) :
x →1
x
⇒ lim f ( ) :
x →1 + 0
f
⇒ lim (1 + ) h :
h → 0
lim 3 (1 + a ) h + b :
h → 0

; :
x
blh izdkj] lim f ( ) :
x →−
10
⇒ lim 5 (1 − a ) h − 2b :
h → 0
⇒
8 :
leh- o dks gy djus ij

: 9 : mÙkj

mnkgj.k 9- iQyu ,d vUrjky 4% 5 esa fuEu izdkj ls ifjHkkf"kr gSµ

0, x = 0

 1 − x, 0< x < 1
 2 2
 1
1

 , x =
 2 2
2 1
 − x, < x < 1
 3 2
1, x = 1


mu fcUnqvksa dks Kkr djks ftu ij iQyu vlarr gSA