Page 159 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math9-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^9 L T[uso ns/ fBwBso L fJZe uo

2
∴ 3x – 12x + 11 = 0 B'N
××
±
−
12 ± 144 4 3 11 12 2 3
x = =
6 6
⇒ x = 2 ± 1
3
1 1
∴ x = 2 + iK x = 2 –
3 3
2
dy
j[D = 6x – 12
dx 2
1
x = 2 + d/ bJh
3
2
dy  1 
= 6 2 +  – 12 = 2 3 XBkswe

dx 2  3 
1
x = 2 + T[Zs/ cbB fBwBso j?.
3
1
ns/ x = 2 – d/ bJh
3
2
dy  1 
= 6 2 −  – 12 = – 2 3 foDkswe

dx 2  3 
2
∴ x = 2 – T[Zs/ cbB T[uso j?.
3
1
j[D fdZs/ j'J/ cbB ftZu x = 2 – gqfs;Ekfgs eoB s/
3
 1   1   1 
2
2
T[uso wkB = 2  − 1 −   − 2 −   − 3 − 
 3   3   3 
 1   1   1  2
1
=  1−   −   −−  =
 3   3   3  33
T[Zso
 x 1/e
1
T[dkjoD 7H f;ZX eo' fe  dk T[uso wkB (e) j?.

x
 x
1
jZb L wzB fbU y = 
x

‘e’ nXko s/ d'jK gZyK dk logarithm b?D s/
 x 1
1
-1
log y = log  = x log = x log x = – x log x
 x
x
‘x’ d/ ;kg/y fBy/VB eoB s/
1 dy  1 
= – x . + 1.log x


y dx  x 
dy
∴ = – (1 + log x)y
dx

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