Page 155 - 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

B'N
jZb ;fjs T[dkjoD

T[dkjoD 1H f;ZX eo' fe sin x + cos x dk T[uso wkB 2 j?.
jZb L wzfBnk y = sin x + cos x
d'jK gZyK dk x d/ ;kg/y fBy/VB eoB s/
dy
= cos x – sin x
dx
d[pkok x d/ ;kg/y d'jK gZyK dk fBy/VB eoB s/

d 2 y
= – sin x – cos x
dx 2

dy
y d/ T[uso ns/ fBwBso wkBK d/ bJh, = 0.
dx
∴ cos x – sin x = 0

iK sin x = cos x
iK tan x = 1
À
iK x =
4
À d 2 y À À
x = T[Zs/ dk wkB = –sin – cos
4 dx 2 4 4
1 1
= – –
2 2
− 2
= =− 2
2

& foDkswe okPh
À
fJ; soQK x = T[Zs/ y dk wkB T[uso j?.
4
À À
y dk T[uso wkB & sin + cos
4 4
1 1
= +
2 2
= 2 .
3
4
2
T[dkjoD 2H cbB x – 8x + 22x – 24x d/ T[usw ns/ fBT{Bsw wkBK d/ bJh x d/ wkB gsk
eo'.
4
2
3
jZb L wzfBnk y = x – 8x + 22x – 24x
d'jK gZyK dk wkB x d/ ;kg/y fBy/VB eoB s/
dy
3
2
= 4x – 24x + 44 x – 24 ....(i)
dx

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