Page 276 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math16-1 IInd 6-8-11 IVth 21-4-12 Vth 20-8-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV oØ ij fLFkr dksbZ fcUnq - yks rFkk eku yks fd
mldh dksfV gSA oØ ij osQ lehi
,d vU; fcUnq 0 δ - 0 δ yks rFkk eku yks fd bldh dksfV gSA
vkSj
ij Øe'k% yEc [khapks rks

, - , 0 δ 1 Y
∴
, δ

f x)
rFkk
, D y =(
, 0 δ 1 ∴ , δ S Q y
P
x x R b
;fn

rFkk
{ks=kiQyksa dks Øekuqlkj C
=
0 δ ls izdV fd;k tk, rks a x
=
δ , {ks=kiQy
2 {ks=kiQy

, x
{ks=kiQy
X O A M N B X
Y
vc
{ks=kiQy ifjek.k esa
rFkk

vk;rksa osQ chp esa fLFkr gS] vFkkZr~
δ 3 δ 3 0 δ δ

δ S
;k 3 < y + y δ ] (δ ls Hkkx nsdj)
x δ

dS
;k , , - ¹tcfd δ → 4 rFkk → 4º
dx

∫ b f ()xdx , ∫ b dS . dx = ∫ b dS = [ ] b
S
vr% a a dx a a
, dk eku tc , 2 dk eku tc ,
, {ks=kiQy

fuf'pr lekdy ,d ;ksx dh lhek 5 gS eku yhft, dksbZ iQyu fdlh vUrjky .
/ esa larr

gS ftldk vkys[k ,d oØ gS ftlesa vkSj dksbZ nks fcUnq gSaA 6v{k ij
vkSj yac gSaA 7 8 rFkk 7 8 Øe'k% fcUnqvksa vkSj osQ Hkqt gSaA vUrjky . - / vFkkZr~
dks] ftldk
eku 2 gS] cjkcj vR;Ur NksVs Hkkxkssa esa ck¡Vk x;k gSA eku yhft, fcUnq o tks oØ ij gSa] osQ
Hkqt Øe'k% 0 rFkk (a + r + 1 ) gSaA
o mudh dksfV;k¡ gSaA bl izdkj lhekUr fLFkfr esa tc
h
→ 4-
,d cgqr gh NksVk vk;r gSA bl vk;r dk {ks=kiQy 0 9 gksxkA bl izdkj ;ksx
osQ 'kCnksa esa ge fuf'pr lekdy
lim h . [ ( f a + ) h + ( f a + 2 ) h + ..... + ( f a + nh )]
n →∞
n
. (a +
, lim ∑ hf rh ),tgk¡ 2 ,
n →∞
r = 1
, ∫ a b f ()xdx ls fu:fir djrs gSaA