07Wa - (15%) . D = n ( x,y ) : x 2 a 2 + y 2 b 2 ≤ 1 o-e...

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27 . 4 . 2008 '` cren ,g"qyz sxeg 2 itpi` ipinipa a`ei :dxend myd aezkle cala legk e` xegy hra ynzydl `p .xfr xneg meya ynzydl oi` .zery yely dpigad jyn .mkicrv z` ahid ehxte ewnp .cenr lk y`xa ...100 "wx" `ed ilniqknd oeivd j` ,103 `ed llekd cewipd .sirq lka riten cewipd !dglvda .zewfg xeh a n x n idi . 1 dl`y xear xcazne | x | < R xear qpkzn xehdy jk R xtqn yiy egiked (15%) ( i ) . | x | > R , ± R zecewpd izya zeqpkzd yi mxeary mixehl ze`nbec e`iad (5%) ( ii ) . ± R zecewpd izyn zg`a weica zeqpkzde , ± R zecewpd izya zexcazd . 2 dl`y . P = ( x 0 ,y 0 ) dcewpa zilia`ivpxtic f ( x,y ) divwpetd :exicbd (4%) ( i ) oeeik lka P -a dxifb f f` P dcewpa zilia`ivpxtic f m` ik egiked (15%) ( ii ) . V oeeika zxfbpl dgqep epze , 0 6 = V R 2 . 3 dl`y dtivx ϕ ( u ) = R β α f ( x,u ) dx ik egiked . [ α,β ] × [ a,b ] oalna dtivx f idz (15%) . [ a,b ] rhwa . 4 dl`y xy`k RR D 1 - x 2 a 2 - y 2 b 2 · 1 2 dxdy lxbhpi`d z` eayg (ziad ixeryl dnec)
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Unformatted text preview: (15%) . D = n ( x,y ) : x 2 a 2 + y 2 b 2 ≤ 1 o-e a,b &gt; . 5 dl`y .oixb htyn z` egqp (4%) ( i ) `ed D = [ α,β ] × [ a,b ] eay ihxtd dxwna oixb htyn z` egiked (15%) ( ii ) .oaln .dxvwa ewnpe zeicbp ze`nbec e`iad .zepekp opi` ze`ad zeprhd . 6 dl`y R ∞-∞ f llkend lxbhpi`d f` ,miiw lim R →∞ R R-R f leabde dtivx f m` (5%) ( i ) .qpkzn f ≡ 7 divwpetl y&quot;na zqpkzn f n zexifbd zeivwpetd zxcq m` (5%) ( ii ) . I rhwa f ≡ divwpetl y&quot;na zqpkzn f n zexfbpd zxcq f` , I rhwa mb f` ,qpkzn ∑ a n xehd m` .miilily-i` mixa` mr xeh ∑ a n idi (5%) ( iii ) .qpkzn ∑ 2 n a 2 n xehd 1...
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