Page 90 - 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 d  1 
dx  x   dk eku D;k gksxk\
() 
1 − 3 1 − 3 1 3 1 3

x 2 − x 2 − x 2
x 2
2 2 2 2

dk osQ lkis{k vody&xq.kkad fdruk gksxk\

# +
+

d
(e x ) = ........
dx
1

e x
d
log x = ........ log e
a
a
dx
1

*
*
x

3-12 lkjka'k % ""

• lim 0 y δ x δ dks iQyu dk osQ lkis{k vody&xq.kkad

4 /
x δ→

" ;k vodyt dgrs gSaA LorU=k pj osQ fdlh izdkj osQ lUnsg ls cpus
y δ d dy
osQ fy, dgk tkrk gS fd iQyu dk osQ lkis{k vody&xq.kkad lim dks ;k
x δ→ 0 δ x dx dx
fy[krs gSaA bl izdkj lhek Kkr djus dh bl fozQ;k dks vodyu djuk dgrs gSa ;k fdlh iQyu osQ
vody&xq.kkad Kkr djus dh lafozQ;k dks vodyu

dgrs gSaA
x
lim ( + f x ) − x f ( )
• ;fn dk dksbZ iQyu vkSj ; δ dk ogh iQyu ; δ gks rks
x → 0 x

dk lhekUr eku ,
* 9 osQ lkis{k dk vody&xq.kkad ;k vodyu

dgykrk gSA

d d d
• D E : N
dx dx dx
• vr% nks iQyuksa osQ ;ksx ;k vUrj dk vody&xq.kkad muosQ vody&xq.kkad osQ ;ksx ;k vUrj osQ cjkcj
gksrk gSA
d
• :

dx
d
•
:
*
vFkkZr~ nks iQyuksa osQ HkkxiQy dk vody&xq.kkad 7

dx