Page 84 - 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 3-9 iQyu ! dk osQ lkis{k vody&xq.kkad] tcfd vk/kj pj ?kkrh; gS

3

!

)$
.

;gk¡ : *

rks ; , : * ; ,

d
vr% * dk osQ lkis{k vody&xq.kkad dx * gSA

d lim log e + (x − ) h log x
e
iqu% * :
dx h →0 h
e
: lim log e (1 + x / ) − hx log x
h →0 h
/ )
e
: lim e + log x e + log (1 hx − log x
h →0 h
<lw=k % * 7# : * 7 ; * #=

/ )
e
: lim log (1 h + hx
→0
h
h − h 2 + h 3 − h 4 + ......
: lim x 2x 2 3x h 3 4x 4
h
→0
 x 2 x 3 x 4 
 log e + (1 = x x − ) + − + ...... 
 2 3 4   

 h h 2 h 3  1
h x −  2 + 3 − 4 + ..... 
: lim  2x 3x 4x 
→0
h
h
: lim   − h + h 2 − h 3 + ......  1 
→0 
h
 x 2x 2 3x 3 4x 4   
: lim  1 − h ×   : 1
→0 
h x
x

 

d 1
∴ * :
dx x
uksV~l * dks
}kjk Hkh fu:fir djrs gSaA