Page 101 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math4-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ y?kqx.kdh; vodyu

uksV
dy
dy
dy 

f
(2 ) +

;k ax 2h x + y +   b   2y  + 2.1 + g 2 . + 0 = 0
 dx   dx  dx
dy
;k 2(hx + by + ) f : 8
; , ;
dx
dy (ax + hy + ) g
∴ : − mÙkj
dx (hx + by + ) f
dy y 2

mnkgj.k 3- ;fn
] rks fl¼ dhft, fd = -
dx 1 − y log x

gy % fn;k gS] : ] y?kqx.kd ysus ij
* : *
nksuksa i{kkssa dk osQ lkis{k vodyu djus ij
1 dy : y . d (log ) + log . dy
x
x
y dx dx dx
1 dy
x
: y . + log .
x dx
 1  dy y
;k  − log x  :
 y  dx x

dy y 2
vr% x : mÙkj
dx 1 − y log x
mnkgj.k 4- ;fn
rks fl¼ dhft, fd
2
dy
sin (a+ y )
dx sin a
sin y
gy % fn;k gS]

:

;k :
sin(a + ) y

vc nksuksa i{kksa dk osQ lkis{k vodyu djus ij
d d
sin (a + y ) . sin y − sin . sin (a + ) y
y
: dx dx
{sin (a + y )} 2
dy dy

;k

; :

;
8

;
dx dx
dy

;k

; : D

;
8

; E
dx
dy

;k

; :

; 8
dx
dy

;k

:

;
dx