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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

2H9 i:kfwsh gfoGkPk (Geometrical Definition) B'N

brkskosk ns/ nbrkskosk (Continuity and Discontinuity)L i/eo fe;h cbB f (x) dk
b/ykfuZso (graph) fyZuD s/ fijVk teo gqkgs j[zdk j?. T[j fJ; soQK j't/ fe fe;h fpzd{ x = a
T[Zs/ N[ZNdk (break) Bk j't/, (Gzr Bk j[zdk j't/) sK cbB f (x) T[; fpzd{ T[Zs/ brksko (continuous)
ejkT[Adk j?.

fJ;d/ T[bN i/eo fe;h fpzd{ x = a T[Zs/ cbB f (x) dk b/ykfuZso N[ZN (break) ikt/ sK fpzd{ x = a
s/ cbB f (x) nbrksko (discontinuous) ejkJ/rk. cbBK d/ fBwB fuZsoK B{z d/y e/ gsk bZrdk j?
fe fuZso (i) ftZu f (x) d/ b/ykfuZso ftZu fpzd{ x = a T[Zs/ fe;h T[ukJh T[dkjoD ti'A k dk fJZe
‘T[Skb’ (jump) j? fe i/eo n;hA b/ykfuZso d/ nB[fdP yZp/ s'A ;Zi/ gk;/ uZb oj/ j'JhJ/ sK x = a
fJZe Gzr (break) j? ns/ ;kB{z x = a tZb d{i/ gk;/ uZbD ftZu g/Af;b B{z T[mkT[Dk gJ/rk. cbB (iii)
dk teo th x = a T[Zs/ Gzr (break) j?. cbB (ii) x = a T[Zs/ Gzr (break) BjhA j? Gkt teo fJ;
soQK j? fe N[ZNdk BjhA j?. fJ; soQK cbB f (x), x = a T[Zs/ brksko j?.
2
T[dkjoD (i) i/eo n;hA cbB y = x dk b/ykfuZso fyZuhJ/ sK
fJj fJZe gotb j[zdk j? fit/A fe fuZso ftZu fdykfJnk frnk
j?. nfij/ cbBK d/ b/ykfuZso T[Zs/ i/eo n;hA ;Zi/ s'A yZp/ iK
yZp/ s'A ;Zi/ fJZe gk;/ s'A d{i/ gk;/ uZbhJ/ sK n;hA e'Jh eqw^Gzr
BjhA gktKr/ ns/ i/eo n;hA b/ykfuZso T[Zs/ fJZe feBko/ s'A d{i/
feBko/ s/ g/Af;b ubkJhJ/ sK ftueko fe;h EK g/Af;b T[mkT[Dh
BjhA gJ/rh. fJj cbB brksko cbB (Continuous function)
j?.

dk b/ykfuZso i/eo n;hA fyZuhJ/ sK d' ftfGzB gotb ns/
fJZe fpzd{ (1, 1) gqkgs j't/rk fit/A fe fuZso ftZu
fdykfJnk frnk j?. fJZE/ i/eo n;hA ;Zi/ s'A yZp/ iK yZp/ s'A
;Zi/ uZbhJ/ sK, x = 1 T[Zs/ eqw Gzr j? ns/ i/eo n;hA x = 1
d/ fJZe gk;/ s'A d{i/ gk;/ g/Af;b uZbkJhJ/ sK x = 1 T[Zs/
g/Af;b B{z T[mkT[Dk (to lift) gJ/rk. fJj cbB nbrksko
(Discontinuous) j?.

n;hA d/yd/ jK fe i/eo fe;h fpzd{ T[Zs/ cbB nbrksko j?
sK T[; fpzd{ T[Zs/ cbB d/ wkB ftZu fJZedw Skb (sudden
jump) j[zdh j? id'Afe brksko cbB dk wkB, x dk wkB pdbD s/ j'bh^j'bh pdbdk j?. fJ; soQK

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