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

noEPk;soh dk rfDs

B'N OM = x, ON = x + δx;
∴ MN = δx
ns/ PM = y,

QN = y + δy; ∴ QR = δy.
i/eo AMPC ns/ ANQC y/socbK B{z
eqwnB[;ko S + δS d[nkok gqrN ehsk ikt/ sK
δS = y/socb ANQC ^ y/socb AMPC &
y/socb MNQP

j[D MNQP y/socb Bshi/ ftZu MNRP
ns/ MNQS nkfJsK d/ ftukb/ ;fEs j?, Gkt

yδx < δS (y + δy) δx

iK ( Bkb Gkt d/ e/) HHHH(1)

iK , [id'A fe ns/ ]

fJ; bJh

& (S dk wkB x = b) ^ (S dk wkB id'A x = a)
& y/socb ABDCH
fBPfus nB[ebB fJZe :'r ;hwk (Limit) j? wzB fbU e'Jh cbB f (x) fe;h nzsok [a, b]
ftZu brksko (Continued) j? fi;dk nkb/y fJZe teo j? fi; ftZu C ns/ D e'Jh d' fpzd{ jB.
x^nZyo T[Zs/ CA ns/ DB bzp jB. ‘a’ ns/ ‘b’ eqw nB[;ko fpzd{nK C ns/ D d/ G{i jB.
nzsokb [a, b] Gkt AB B{z, fi;dk wkB (b – a) j?, n pokpo pj[s S'N/ GkrK ftZu tzfvnk frnk
j?. wzB fbU fpzd{ P s/ Q fijV/ teo T[Zs/ jB, d/ G[i eqw nB[;ko (a + rh) ns/
jB. PM s/ QN T[jBK dhnK e'NhnK jB. fJ; soQK ;hwKs ;fEsh ftZu id'A , PRNM
fJZe pj[s jh S'Nk nkfJs j?. fJ; nkfJs dk y/socb f (a + rh) × h j't/rk. fJ; soQK :'r d/
PpdK ftZu n;hA fBPfus nB[ebB

B'N; T[j g{oD y/socb j? fijVk teo y = f (x), x^neP ns/ x = a s'A x
= b ;hwktK d/ nzdo pDdk j?.

Teo y = f (x), x^neP ns/ o/yktK x = a ns/ x = b Bkb fxo/ y/so ABCD dk y/socb
fBwB ;{so d[nkok gsk ehsk iKdk j?L

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