Page 88 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math3-1 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 x n
mnkgj.k 3- iQyu dk osQ lkis{k vody&xq.kkad Kkr dhft,A
log x
e
d n n d
d   x n   log x dx x − x dx log x
e
e
gy %   :
dx  log x  (log x ) 2
e  
e
.
log xnx n − 1 − x n . 1 nx n − 1 log x − x n − 1
e
: x : e
(log x ) 2 (log x ) 2
e
e
x n − 1 (log x − 1)
n
: e mÙkj
(log x ) 2
e
x
mnkgj.k 4- ;fn rks fl¼ dhft, fd
x +5
dy

dx
x
gy % fn;k gS] :
x + 5
(x + 5) . d ( ) x − x . d (x + 5)
dy dx dx (x + 5).1 − x .1
∴ : =
dx (x + 5) 2 (x + 5) 2
x + 5 − x 5 dy 5x
: = ⇒ x =
(x + 5) 2 (x + 5) 2 dx (x + 5) 2
x  x  x  5  5x
rFkk 8 :  1 −  =   =
x + 5  x + 5  x + 5 x +  5  (x + 5) 2
vr% (1) vkSj (2) ls]
dy
: 8 mÙkj
dx

iz'ukoyh )")

fuEufyf[kr iQyuksa dk osQ lkis{k vody&xq.kkad Kkr dhft, %
1 x n
" #"
x 1/ 4 log x
e
x x 2
)" a + x 2 '" e + x 2
2
2
e x e x
" 2 +" x
1 + x 1 + e
x 3  a 
" ;fn : 9 rks ′   dk eku Kkr dhft,A
2
a − x 2  2 