Page 52 - 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  x 2   
: lim 2 1 +  + ....    < ≠ -=
x → 0   3!  

: mÙkj

e x −
mnkgj.k 12- lim dk eku Kkr dhft,A
x 0 x
 1 + x + x 2 + x 3 .... ∞  − 1
x
e − 1   2! 3!  
gy % lim : lim
x → 0 x x → 0 x
 x 2 x 3   x x 2 
 x + 2! + 3! + .... ∞  x  1 + 2! + 3! + .... ∞ 
: lim   : lim  
x → 0 x x → 0 x
 x x 2 
: lim   + 1 2! + 3! + ∞ ....  
→a
x
: tc ≠ - : mÙkj

1 + 2+ 3+ .... + x
mnkgj.k 13- lim dk eku Kkr dhft,A
x x 2
1 + 2 + 3 + .... + x xx 1)
( +
gy % lim 2 : lim 2
x →∞ x x →∞ 2x
2  1  1
x  1 +  1 +
: lim  x  : lim x
x →∞ 2x 2 x →∞ 2

1  1 
: .  lim = 0 
2  x →∞ x 
1
vr% vHkh"V eku : . mÙkj
2
a x − b x a
mnkgj.k 14- fl¼ dhft, fd lim = log .
x 0 x e b
a x b x
;k lim dk eku Kkr dhft,A
x 0 x

gy % Li"V gS tc : - rks va'k rFkk gj nksuksa 'kwU; gks tkrs gSaA vr%
rFkk dk ,DliksusUVh izes; dh
lgk;rk ls izlkj djus ij]
a − b x e x log e a − e x log e b
x
ck;k¡ i{k : lim : lim
x → 0 x x → 0 x
x
x
 (log a ) 2   ( log b ) 2 
 1 + x log a + e 2! e + .... −   1 + x log b + e 2! e + .... 
: lim    
x → 0 x