Page 78 - 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
3-5 dk osQ lkis{k vody&xq.kkad

3

eku yks : gks rks ; , : ; ,
d

vr% dk osQ lkis{k vody&xq.kkad gSA
dx
d (x + ) h n − x n

∴ : lim
dx h → 0 h
(1 +
/ ) −
: lim hx n 1 , dks ckgj fudkydjA

h → 0 h
h

vc pw¡fd , → -9 ge dks bdkbZ ls NksVk eku ldrs gSaA vr% # osQ lHkh ekuksa osQ fy, ; ,6 dk f}in
x
izes; R
, F/ , ls izlkj djus ij
d x n   h ( n n − 1) h 2  

dx : lim 0 h   + x + . n 1.2 x 2 + − ..... 1  1   
h →
x  n  h ( n n − 1) h 2  
: lim  . n + . + ..... 
h → 0 h  x 1.2 x 2   

: lim   n + ( n n − 1) h + .....  
h → 0  x 1.2x 2 
 n 
: lim  + h ×
(



h → 0  x 
: #
9 D;ksafd , → -
d

∴ #
dx
d
bldk ,d fof'k"V ifj.kke ;g gS] :
dx
d d

mnkgj.k 1- (9
"
"
+) "
dx dx
d d

mnkgj.k 2- +
+
+"#
# "
dx dx
d   1 = d (x -1/2 ) 1 1
mnkgj.k 3-  

"
dx   x dx 2 2

d 6
)

VkLd (5x dk eku Kkr djsaA (mÙkj % )% )
dx