Page 173 - 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

1 uksV
( izfrLFkkfir djus ij
e
2
dy ( * A , +B) dy ( +
dx 2 dx

2
dy 1
e
dx 2 ( * Í.kkRed gSA ∴ ( osQ fy, iQyu mfPp"B gSA
1
∴ fufnZ"V iQyu esa ( izfrLFkkfir djus ij
e

 1  1/ e


mfPp"B eku ( 1  ( fl¼ gqvkA
 
 e 
log x
mnkgj.k 8- dk mfPp"B eku Kkr djks] tcfd
3 3
x
log x
gy % eku yks (
x
x
dy x .(1/ ) − (log ).1 1 − log x
x
∴ ( (
dx x 2 x 2
2
dy ( 2 − x − (1/ ) x (1 − log ).2x
x
dx 2 x 4
− − x + 2x 2 log x 2 log − x 3
x
( =
x 4 x 3
dy 1 − log x
dx ( + j[kus ij] x 2 ( + ;k * . ' ( +

;k . ' ( ( . '
∴ (
2
dy − 2log e 2 − 3 3 1
( ij] 2 ( = = − ( Í.kkRed gSA
dx e 3 e 3 e 3
∴ ( , ij iQyu mfPp"B gS rFkk
log e 1
bldk mfPp"B eku ( = mÙkj
e e

mnkgj.k 9- ;fn 4 osQ ! % vkSj # ij mfPp"B&fufEu"B eku
1 . . 5 gSa rks vkSj osQ eku Kkr dhft,A

dy 1
gy % ( ( . ' , , ⇒ ( , ,

dx x
dy
mfPp"B&fufEu"B osQ fy,] ( +)
dx