Page 51 - 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

bdkbZ lhek o lrrrk

m    m (m − 1) h 2   uksV

h
a  1 + m  + 2  + .... 1  −
a
a
: lim      
h→ 0 h
m  m m (m − 1) h 
ah  + 2 + .... 
: lim  a 2 a 
h→ 0 h
m m m (m − 1) h 

: lim a  + + .... , (h ≠  0)
h→ 0  a 2! a 2 
m m − 1
: a × = ma : nk;k¡ i{kA
m
a
fVIi.kh % ;g chth; iQyu dh lhek Kkr djus osQ fy, izeq[k lw=k osQ :i esa iz;qDr gksrk gSA

 p  x
mnkgj.k 9- lim 1 +  dk eku Kkr dhft,A

x 0  x 
 p  x
gy % lim 1 + 

x →∞  x 
 1  x
miizes; lim 1 +  : osQ iz;ksx ls

x →∞  x 
 p  x   p   / xp   p

lim 1 +  : D;ksafd lim  1 +   = e p . mÙkj

x →∞  x  / xp→∞  / xp     
  log x
lim  
mnkgj.k 10- x 1  1 − x  dk eku Kkr dhft,A

gy % : ; , j[kks] tcfd , cgqr gh NksVk gSA
h 2 h 3
log x log (1 + ) h h − 2 + 3 − ....
vr% lim : lim = lim
x → 1 1 − x h→ 0 − h h→ 0 − h
 h h 2 
: lim − 1 −  + − ....  tc , ≠ - : 8 mÙkj
h→ 0  2 3 

e x − e -x
mnkgj.k 11- lim dk eku Kkr dhft,A
x 0 x
x
e − e − x 1  x 2 x 3   x 2 x 3  
gy % lim : lim 1 +  x + + + .... −   1 − x + − + ....  
x → 0 x x → 0 x  2! 3!    2! 3!  
1  x 3   
: lim 0 x  2 x +   3! + ....     
x →