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VED1
E L-LOVELY-H math9-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N  3 
4 −
=−     = 2 3 XBkswe
 2 
2π
∴ x = T[Zs/ cbB fBwBso j?.
3
2π
ns/ x = gqfs;Ekfgs eoB s/, cbB dk fBwBso wkB
3
2π 4π 2π 3 4π− 33
= + sin = − = T[Zso
3 3 3 2 6

;t?^w[bKeD (Self Assessment)

fBwBfbys eEBK ftZu ;Zu iK M{m dh gfjukD eo'
(State whether the following Statements are True or False) –
2
dy
5H T[uso d/ bJh x = a T[Zs/ dk wkB XBkswe j[zdk j?.
dx 2
2
dy
6H fBwBso d/ bJh x = a T[Zs/ dk wkB XBkswe j[zdk j?.
dx 2
7H cbB d/ d' ;wkB wkBK d/ ftukb/ xZN s'A xZN fJZe T[uso iK fBwBso wkB io{o j[zdk
j?.
dy
8H cbB d/ T[uso iK fBwBso fpzd{nK T[Zs/ dk fuzBQ BjhA pdbdk j?.
dx

9H6 ;koKP (Summary)

• i/eo s[jkv/ wekB dh T[ukJh nrb^prb (;Zi/ ns/ yZp/) ftZu ;fEs d'jK wekBK dh
T[ukJh s'A tZX j? sK s[jkv/ wekB dh T[ukJh T[uso (Maximam) ejkJ/rh ns/ i/eo
s[jkv/ wekB dh T[ukJh nrb^prb (;Zi/ ns/ yZp/) ftZu ;fEs d'B'A wekBK dh T[ukJh
s'A xZN j? sK s[jkv/ wekB dh T[ukJh fBwBso (Minimam) ejkJ/rh.
• cbB ;[szso uo d/ fe;h fBPfus fpzd{ T[Zs/ xNdk j? ns/ T[; s'A nrb/ wkBK d/ bJh
tZXdk j? sK xNdh j'Jh ;fEsh ftZu tXD tkbh ;fEsh d/ nkT[D ftZu cbB fBwBso
wkB gqkgs eodk j?.

• T[uso wkB d/ pknd fBwBso wkB ns/ fBwBso wkB d/ pknd T[uso wkB nkT[Adk
j? Gkt T[uso ns/ fBwBso wkB J/eKso eqw Bkb nkT[Ad/ jB.

2
dy
• i/eo x d/ fe;h wkB d/ bJh dk wkB XBkswe j? sK cbB T[; x d/ wkB d/ bJh
dx 2
fBwBso j't/rk i/eo foDkswe j't/ sK T[uso j't/rk.

9H7 Ppde'P (Keywords)

• T[uso (Maximum) ^ tZX s'A tZX.
• fBwBso (Minimum) ^ fBT{Bsw.

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