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VED1
E L-LOVELY-H math2-2 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^2 L ;hwk ns/ brkskosk

• i/eo fe;h cbB f (x) dh x = a T[Zs/ dZyD gZy ns/ tkw gZy d'B'A ;hwktK Pkfwb ns/ fJZe B'N
;wkB j'D, sK cbB f (x) dh x = a T[Zs/ ;hwk dk ti{d j[zdk j?.
lim ( )fx = lim ( ) = (wzB fbU)
fx
l
x→ a + x→ a -
• fJZE/ l cbB dh ;hwk ejkT[Adh j? ns/ fJ;B{z n;hA j/m nB[;ko ftnes eod/ jK^
lim ( )fx = H
l
x→ a
• ;kB{z ;hwk gsk eoB d/ bJh dZyD gZy s/ tkw gZy d'B'A ;hwktK gsk eoBhnK ukjhdhnK
jB gozs{ wZXfwe ;so s/ n;hA ;hwk eJh tko f;ZX/ jh gsk eod/ jK.

• nzP ns/ jo d'jK B{z T[;d/ T[GfBPm r[Dbyzv fijV/ Iho' BjhA jB, Bkb Gkr d/Dk s[ozs
;zGt Bk j't/ sK Pq/Dh gq;ko (expansion in series) iK fe;h o{gKsoD (transformation) d/
pknd fJj fefonk ;zGt j' ;edh j?.
• 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?.
• cbB f (x) fe;h fttfos nzsokb (a, b) ftZu brksko fejk iKdk j? i/eo fJj nzsokb
(a, b) ftZu x d/ ;ko/ wkBK d/ bJh brksko j?.
• cbB f (x) fe;h pzd nzsokb (closed interval) [a, b] ftZu brksko fejk iKdk j?, i/eo
(i) fJj x d/ T[jBK ;ko/ wkBK d/ bJh brksko j't/ fi;d/ bJh a < x < b
(ii) lim f (x) = f (a) (iii) lim f (x) = f (b)H
x→ a+ 0 x→ b+ 0

2H16 Ppde'P (Keywords)
• eqw (Sequence)^eqw, f;bf;bk.

• ;ss (Continually)^brksko.

2H17 nfGnk; gqPB (Review Questions)

 x − 2ax a 
2
2
+
1H lim   dk wkB gsk eo'. (T[Zso L –a)
−
x→ 0  xa 
x
a − b x a
2H f;ZX eo' fe lim = loge H
x→ 0 x b
x − 1
3
3H lim dk wkB gsk eo'. (T[Zso L 3)
x→ 1 x − 1
4H cbB dh brkskosk dk gqhyD eo'. (T[Zso L nbrksko)

5H do;kU fe ()fx = , x x = T[Zs/ brksko j?.
0

T[Zso L ;t?^w[bKeD (Answer : Self Assessment)

1H (i) dZyD gZy ;hwk (ii) tkw gZyh ;hwk (iii) ti{d (iv) ;hwKs (v) wZXfwe.
2H (i) (a) (ii) (b) (iii) (c) (iv) (a) (v) (c)

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