Page 175 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

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

bdkbZ mfPp"B vkSj fufEu"B % ,d pj

2 π uksV
∴ ( ij iQyu fufEu"B gSA
3
2 π
vkSj ( izfrLFkkfir djus ij] iQyu dk fufEu"B eku
3
2 π π 2 π 4 4 π − 3 3 3
( + = sin − = mÙkj
3 3 3 2 6

Lo&ewY;kadu

fuEufyf[kr dFkuksa esa lR; vFkok vlR; dh igpku djsa
# .. #
'

6 .
2
dy
5- mfPp"B osQ fy, ( ij 2 dk eku /ukRed gksrk gSA
dx
2
dy
6- fufEu"B osQ fy, ( ij dk eku /ukRed gksrk gSA
dx 2
7- iQyu osQ nks leku ekuksa osQ eè; de ls de ,d mfPp"B ;k fufEu"B eku vo'; gksrk gSA
dy
8- iQyu osQ mfPp"B ;k fufEu"B fcanqvksa ij dk fpÉ ugha cnyrk gSA
dx

9-6 lkjka'k

• ;fn vkiosQ edku dh Å¡pkbZ vxy&cxy (nk,¡ vkSj ck,¡) esa fLFkr nksuksa edkuksa dh Å¡pkbZ ls vf/d
gS rks vkiosQ edku dh Å¡pkbZ mfPp"B - D dgyk;sxh vkSj ;fn vkiosQ edku dh Å¡pkbZ
vxy&cxy (nk,¡ vkSj ck,¡) esa fLFkr nksuksa edkuksa dh Å¡pkbZ ls de gS rks vkiosQ edku dh Å¡pkbZ
fufEu"B -
dgyk;sxhA
• iQyu LorU=k pj osQ fdlh fuf'pr fcUnq rd ?kVrk gS vkSj mlls vxys ekuksa osQ fy, c<+rk gS rks ?kVrh
gqbZ fLFkfr ls c<+us okyh fLFkfr osQ vkus esa iQyu fuEure eku izkIr djrk gSA
• mfPp"B eku osQ ckn fufEu"B eku vkSj fufEu"B eku osQ ckn mfPp"B eku vkrk gS vFkkZr~ mfPp"B vkSj
fufEu"B eku ,dkUrj Øe ls vkrs gSaA

2
dy
• ;fn osQ fdlh eku osQ fy, 2 dk eku /ukRed gS rks iQyu ml osQ eku osQ fy, fufEu"B gksxk
dx
rFkk ;fn Í.kkRed gks rks mfPp"B gksxkA

9-7 'kCndks'k

• mfPp"B - D vf/dreA

• fufEu"B -
fuEureA