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VED1
E L-LOVELY-H math7-1 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
j[D, N fpzd{ T[Zs/ Ykb (Slope)

j[D HHHHH(i)

:{bo; gqw/:,

iK HHHHH(ii)

fiZE/ P = e[ZbQ T[sgkdB ;so

iK QN = NG + QG

fJ; soQK e[ZbQ T[sgkdB QN, NG ns/ OG GkrK ftZu tzv j[zdk j?. fiZE/ NG ns/ QG eqw
nB[;ko L ;kXB ns/ K B{z fdZs/ ikD tkb/ g[o;eko jB. fJ; soQK i/eo fe;h cow d/ jo/e
;kXB B{z T[;dh ;hwKs T[sgkdesk d/ pokpo g[o;eko fdZsk iKdk j? sK e[ZbQ T[sgkdB g{oh soQK
ysw j' ikDr/.

7H2H2H :{bo; gqw/: dk rDhse jZb
(Mathematical Solution of Eulers Theorem)
:{bo; gqw/: ;wo{g cbB dh ;jkfJsk d[nkok ;hwKs T[sgkdesk d/ f;XKs ftZu fJZe ftP/P
;zpzX B{z dZ;dh j?. i/eo u = f (x, y) fJZe h e'fN dk ;wo{g cbB j? sK fJj gqw/: nZr/ fby/
;zpzX B{z do;kT[Adh j?^

= xf tx + yf ty

fiZE/ L.H.S. yZpk j? ns/ R.H.S. ;Zik j? sK L.H.S. = R.H.S.
h-1
xf tx + yf ty = ht f (x, y)
fJ; soQK i/eo t = 1 sK, t dh e[ZM ;zfynk j' ;edh j?.
xf x + yf y = hf (x, y)
h ;wheoD dh e'fN j?. i/eo n;hA ;wo{g cbB b?Adk jK sK h = 1
sK xf x + yf y = f (x, y)

u ∂ u ∂
iK x + y = u
x ∂ y ∂
i/eo d{ik e'fN ;wheoD b?Ad/ jK sK fJj j't/rk
u ∂ u ∂
x + y = 2u
x ∂ y ∂

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