Page 100 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math4-1 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
dy 1
5- ;fn
log x + log x + log x + ... + ∞ rks fl¼ dhft, fd dx = x (2y − 1)

6- ;fn y = x + 2 1 1 rks fl¼ dhft, dy = 2xy 2 2 -
2
x + dx 1 + y
2
x + ......

4-3 vLi"V iQyu "

;fn vkSj osQ chp dksbZ ,slk lehdj.k fn;k gks ftls rqjUr osQ fy, gy ugha fd;k tk losQ] rks dks
dk vLi"V iQyu ,"

dgrs gSaA blosQ foijhr ;fn dk eku osQ :i esa Kkr fd;k
tk losQ] rks dks dk Li"V iQyu !"

dgrs gSaA

D;k vki tkurs gSa vLi"V iQyu dk vodyuµfdlh vLi"V iQyu ,"

ls

J
dk eku Kkr djus osQ fy, fn;s gq, lehdj.k osQ izR;sd in dk osQ lkis{k
vodyu djks rFkk fiQj
J
osQ in ,d vksj djosQ mldk eku Kkr dhft,A

gy lfgr mnkgj.k

dy

mnkgj.k 1- ;fn #
% rks Kkr dhft,A
dx
gy % fn;k gS%
; , ; : -

osQ lkis{k vodyu djus ij
a . d (x 2 ) + 2h d (xy + ) b . d (y 2 ) = 0
dx dx dx
 dy  dy

;k 2ax + 2h x . + y .1 +  2by . = 0
 dx  dx
dy
;k 2(hx + by ) : 8
; ,
dx
dy  ax + hy 
∴ : 8   mÙkj
dx  hx + by 

dy

mnkgj.k 2- ;fn # # #
% rks Kkr dhft,A
dx
gy % fn;k gS]
; , ; ; ; ; : -

osQ lkis{k vodyu djus ij
d d d d d d
g
f
h
a (x 2 ) + 2 . (xy + ) b . (y 2 ) + 2 . () + x 2 . () + y ( ) = c 0
dx dx dx dx dx dx