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VED1
E L-LOVELY-H math3-1 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 gq;sktBk (Introduction)

2
wzB fbU y = x
id'A x = 2, sK y = 4, id'A x = 3, y = 9.
X, 2 s'A tZX e/ 3 j' iKdk j? sK y th 4 s'A tZX e/ 9 j' iKdk j?. e'Jh uo fezBk tZXdk j? T[;B{z
T[;d/ tkX/ (Increment) efjzd/ j?. x d/ tkX/ B{z brGr δx d[nkok ;{fus eod/ jK ns/ ‘v/bNk
n?e;’ (delta x) efje/ gVQd/ jK.
T[go'es T[dkjoD ftZu δx = 3 – 2 = 1 ns/ δy = 9 – 4 = 5
i/eo x, 1 s'A pdbe/ H8 j' ikt/ sK δx = .8 – 1 = – 2H

B'N; fJj fXnkB oZyDk ukjhdk j? fe δx eoe/ noE = δ × x BjhA j? Gkt fJj δ ns/ x
dk r[DBcb Bk j' e/ fJZe gqshe (Symbol) j?. fJj J/eb okPh j?.

fJj th ;gPN j? fe i/eo ;[szso uo dk wkB x s'A pdbe/ x + δx j' ikt/ sK goszso uo dk
wkB th y s'A pdbe/ y + δy j' ikt/rk.

3H1 fBy/VB^r[DKe iK fBy/VBk (Differential Coefficient)
2
wkB fbU y = x , x dk cbB j?. wkB fbU x dk nozGe wkB 3 j?.
j/mbh ;koBh ftZu fdykfJnk frnk j? fe x ftZu tkXk δx j'D s/ y ftZu tkXk δy ns/ fJjBK

tkfXnK ftZu nB[gks d/ wkB ftZu fe; soQK gfotosB j[zdk j?. fJZE/ x d/ nozGe wkB 3

ftZu 4, 3, 2, 1, HHHHHHH nkfd dk tkXk fbnk frnk j?.

δx BtK x (x + δx) BtK y (y + δy) δy

4 7 49 40 10
3 6 36 27 9
2 5 25 16 8

1 4 16 7 7
0.1 3.1 9.61 .61 6.1
0.01 3.01 9.0601 .0601 6.01
0.001 3.001 9.006001 .006001 6.001

0.0001 3.0001 9.00060001 .00060001 6.0001
2
2
h 3 + h 6 + 6h + h 6h + h 6 + h

fJ; ;koDh s'A ;gNP j? fe
1H fit/A^fit/A δx S'Nk j' e/ Iho' tZb nZr/ tXdk j? (approaches zero) T[t/A^T[t/A δy th S'Nk j' e/
Iho' d/ tZb nZr/ tXdk j?.

Gozs{ fJjBK d'jK dk nB[gks S'Nk j'D s/ th Iho' d/ tZb nZr/ tXD d/ ;EkB s/ fJZe ;fEo

wkB d/ tZb/ nZr/ tZXdk j? fijVk fJ; T[dkjoD ftZu 6 j?.

64 LOVELY PROFESSIONAL UNIVERSITY