Page 167 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math9-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ mfPp"B vkSj fufEu"B % ,d pj

2
dy uksV
;fn osQ fdlh eku osQ fy, dk eku /ukRed gS rks iQyu ml osQ eku osQ fy, fufEu"B gksxk rFkk
dx 2
;fn Í.kkRed gks rks mfPp"B gksxkA

3
2
dy dy
( ;fn osQ fdlh eku osQ fy, ( + gks rks ml osQ eku osQ fy, 3 Kkr djukA ;fn ml
dx 2 dx
3
dy
osQ eku osQ fy, ≠ + rks iQyu dk eku ml osQ eku ij u rks mfPp"B vkSj u fufEu"B gksxkA
dx 3
3
4
dy dy
(
;fn fdlh osQ eku osQ fy, ( + rks ml osQ eku osQ fy, Kkr dhft, ;fn ml osQ
dx 3 dx 4
4
dy
eku osQ fy, 4 Í.k gS rks ml osQ eku ij iQyu mfPp"B gS vkSj ;fn /u gS rks fufEu"B gksxkA ;fn ;g
dx
Hkh 'kwU; gS rks blh izdkj vkxs fØ;k djrs tkuk gSA

gy lfgr mnkgj.k

mnkgj.k 1- fl¼ dhft, fd
dk mfPp"B eku 2 gSA

gy % ekuk (

,
nksuksa i{kksa dk osQ lkis{k vodyu djus ij
dy
dx (
*
iqu% osQ lkis{k nksuksa i{kksa dk vodyu djus ij
2
dy ( *

*
dx 2
dy
osQ mfPp"B vkSj fufEu"B ekuksa osQ fy,] ( +
dx
∴
*

( +

;k

(
;k
(
π
;k (
4
2
π dy π π
( ij dk eku ( *

*
4 dx 2 4 4
1 1
(* −
2 2