Page 54 - 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 lim : lim :
x →+ 0 x →− 0
1
1
vr% lim :
x → 1
mnkgj.k 18- iQyu fuEu izdkj ls ifjHkkf"kr gS%
 1
 x, 0 x < 2



 0, x = 1
 2
 1
 1 − x, < x 1
 2

lim dk eku Kkr dhft,A
x
 1 
gy % O 3 :  + 0 =  lim f ( ) x
 2  x → 1/2 + 0
 1   1  1   1
: lim f  + h : lim 1 −  − h : lim  − h = 


h→ 0  2  h→ 0  2  h→ 0  2  2
 1   1 
3 O 3 : f  − 0 =  lim fx  − h 
( ) : lim f
 2  x → 1/2 − 0 h→ 0  2 
 1  1
: lim  − h = 
h→ 0  2  2
∴ O 3 : 3 O 3

1
fx
vr% lim ( ) = . mÙkj
x → 1/2 2
iz'ukoyh 012

fuEufyf[kr dk eku Kkr dhft, %
x

lim % 8 ; lim e − 1 .
x → 0 x → 0 e x
e x /2 − 1 x − 1
3
lim . lim .
x → 0 x x → 1 x − 1
x − 4 e −− x
2
x
1
lim . # lim .
x → 2 x − 2 x → 0 x 2
% lim y 2 tgk¡ y = 2 ax + bx + 2 cx 3 . ' lim x 2
x → 0 x x →∞ 1 + x 2

tanθ x − a 4
4
+ lim - lim .
2
θ→ 0 θ x → a x − a 2