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VED1
E L-LOVELY-H math2-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^2 L ;hwk ns/ brkskosk

jZb L f (x), x = 0 T[Zs/ brksko (continuous) j? feT[Afe f (0) = 1, (fdZsk j?) B'N

sin x
1
ns/ lim == f (0)
x→ 0 x

jZb L f (x), x = 0 T[Zs/ nbrksko (discontinuous) j? feT[Afe f (0) = 1

ftnkfynkswe T[dkjoD

T[dkjoD 1H

dk nkb/y fyZu'.

f;ZX eo' fe cbB w{bfpzd{ T[Zs/ nbrksko
(discontinuous) j?.
jZb L f (x) dk nkb/y fyZuDk nfs ;ob j?. fJj fuZso
ftZu fdykfJnk frnk j?. ;gPN j? fe fpzd{ x = 0 T[Zs/
nkb/y ftZu fJZe T[Skb (jump) j?. j[D n;hA dZyD gZy ns/
tkw gZy ;hwktK dh iKu eod/ jK.
w{bfpzd{ (x = 0) T[Zs/ dZyD gZy ;hwk (R.H.L.):
x ≥ 0 d/ bJh,

∴ HHHH(i)

w{bfpzd{ T[Zs/ tkw gZy ;hwk (L.H.L.) (x < 0 d/ bJh)
x < 0 d/ bJh,

∴ HHHH(ii)
fJ; soQK (i) ns/ (ii) s'A
fJ; soQK x = 0 T[Zs/ cbB f (x) nbrksko (discontinuous) j?.
(B'NL ftfdnkoEhnK B{z ukjhdk j? fe T[j do;kT[D fe x = 0 T[Zs/ f (x) dZyD brksko j?.)

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