Page 102 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math5-1 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
fsZik ntebi d  d y  dy 3
2
3

dx dx 2  = dx 3  f ′′′ (x), D y, y 3

HHHHHHHHHHHHHH HHHHHHHHHHHHHHHH HHHHHHHHHHHHHHHH
d  d n -1 y  dy
n
ntK ntebi  -1  = f (x), D y, y n
n
n
dx dx n  dx n


6
7
fJ; soQK i/eo y = x , sK dy = 7x
dx

ns/

jZb ;fjs T[dkjoD

3
4
5
2
T[dkjoD 1H i/eo f (x) = ax + bx + cx + dx + ex + f sK ′′′′ (x) dk wkB gsk eo'.
f
jZb L fdZsk j?,
5
4
3
2
f (x) = ax + bx + cx + dx + ex + f
4
3
2
f ′ (x) = 5ax + 4bx + 3cx + 2dx + e + 0
3
2
f ′′ (x) = 20ax + 12bx + 6cx + 2d + 0
2
f ′′′ (x) = 60ax + 24bx + 6c + 0
f ′′′′ (x) = 120ax + 24b. T[Zso
T[dkjoD 2H i/eo y = A sin mx + B cos mx sK f;ZX eo' fe
2
dy
2
+ m y = 0H
dx 2
jZb L fdZsk j?, y = A sin mx + B cos mx
x d/ ;kg/y fBy/VB eoB s/,

x d/ ;kg/y d[pkok fBy/VB eoB s/,

fJ; soQK

2
T[dkjoD 3H i/eo y = sin (sin x), sK f;ZX eo' fe y 2 + y 1 tan x + y cos x = 0H
jZb L fdZsk j?, y = sin (sin x)

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