Page 87 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math3-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ vodyu

va'k esa dks tksM+us vkSj ?kVkus ij uksV

( ) { (x +
x
fx
x
1
: lim 0 f 2 () { (x + f 1 ) h − hf 1 2 ( )} − (x + fx ( ) f 2 ) h − f 2 ( )}
h→
x
) h f
2
 ( f x + ) h − f ( ) x f  (x + ) h − f ( ) x
fx 1 1  − f 1 ()  x 2 2 
() 
2
: lim  h   h 
h→ 0 fx h f 2
( +
) ( ) x
2
f 2 () x . d f 1 () x − f 1 () x d f 2 () x
: dx dx
fx
[( )] 2
2
vFkkZr~ nks iQyuksa osQ HkkxiQy dk vody&xq.kkad 22" 22"
− −

:

Denr. (Diff. coeff. of Numr.) − Numr. (Diff. coeff. of Denr.)
:
Square of Denominator
u
D;k vki tkurs gSa  ;fn : rks 
 v 
  
 v du − u dv 
 dy dx dx 
  dx : v 2  
gy lfgr mnkgj.k
e x dy
mnkgj.k 1- ;fn
rks dk eku Kkr dhft,A
x dx
d x x d
dy x dx e − e dx x xe − x e x .1 e x (x − 1)
gy % : : = mÙkj
dx x 2 x 2 x 2
d   sin x
mnkgj.k 2- dx   log x   dk eku Kkr dhft,A
e
d
d
d  sin x  log x . dx (sin ) x − sin x . dx (log x )
e
e
gy % dx   log x  
(log x ) 2
e
e
1
(log x . ) cos x − (sin . ) x
e
: x
(log x ) 2
e
x log x cos x − sin x
: e mÙkj
x (log x ) 2
e