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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

noEPk;soh dk rfDs

B'N (ii) i/eo f (x) ns/ g (x) d'B'A fe;h fpzd{ x = a T[Zs/ brksko jB sK f (x) g (x) th x = a
T[Zs/ brksko j't/rk.
(iii) i/eo f (x) fe;h fpzd{ x = a T[Zs/ brksko j? ns/ k fJZe fBPfus n;b ;zfynk j? sK
k f (x) th x = a T[Zs/ brksko j't/rk.
fx
()
(iv) i/eo f (x) ns/ g (x) fe;h fpzd{ x = a T[Zs/ brksko j? ns/ g (a) ≠ 0 sK th x
()
gx
= a brksko j't/rk.
1
(v) i/eo f (x), x = a T[Zs/ brksko j? ns/ f (a) ± 0 sK th x = a T[Zs/ brksko
()
fx
j't/rk.
(vi) i/eo f (x), x = a T[Zs/ brksko j? sK fx th x = a T[Zs/ brksko j't/rk.
()
2
T[dkjoD 1H fdykU fe cbB f (x) = x + 1, x = 2 T[Zs/ brksko j?.
jZbL lim f (x) = 5 = f (2).
x→ 2
fJ; soQK cbB x = 2 T[Zs/ brsko j?.
1
T[dkjoD 2H cbB f (x) = , x = 2 T[Zs/ nbrksko j?. f;ZX eo'.
x − 2
jZbL (i) f (2) gfoGkfPs BjhA j? (jo Iho' j?).
(ii) lim f (x) dk ti{d BjhA j? (∞ d/ pokpo j?).
x→ 2
x = 2 B{z SZv e/ pkeh jo fpzd{ T[Zs/ cbB brksko j?. fJ; soQK
x = 2 T[Zs/ cbB nbkrkskosk (discontinuity) j?.
x 2 − 4
T[dkjoD 3H fdykU fe cbB f(x) ,x =2 T[Zs/
x − 2
nbrksko
(discontinuous) j?.

jZbL (i) f (2) gfoGkfPs BjhA j? (nzP ns/ jo d'B'A Iho'
jB).
(ii) lim f (x) = 4.
x→ 2
fJ; soQK cbB x = 2 nbrksko j?.
T[dkjoD 3 ftZu nbrkskosk B{z d{o ehsk ik ;edk j? feT[Afe
x − 4
2
cbB B{z d[pkok () = , x ≠ l gfoGkfPs eoe/ f (2)
2
fx
x − 2
= 4.
x − 4
2
f (x) ns/ g (x) = x + 2 d/ rqkc ;wkB jB id'A fe gfjb/ ftZu S/d (hole) j?.
x − 2
T[dkjoD 2 ftZu brkskosk B{z d{o BjhA ehsk ik ;edk feT[Afe ;hwk dk th ti{d BjhA j?.

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