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infi2HW14

# infi2HW14 - γ xy`k 4 libxz-nxt `id d`ad divfixhnxtdy...

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14 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2008 lixt`l 20 :dybd jix`z A 4 lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz sca jxev oi` .oeilib xtqne ,f"z ,zeny xexiaa oiivl `p .wcedn yibdl `p .mixqlw e` zeiwy `ll .xry 1 libxz dci`elwivd :dxrd . 0 t 2 π xear γ ( t ) = ( a ( t - sin t ) ,a (1 - cos t )) dci`elwivd jxe` z` eayg 'mi`ex' mz` m`d) menipinl menipinn a qeicxa akx binv zty lr dcewp dyery lelqnd `id .(?z`f 2 libxz . f ( x,y ) = x 3 + xy 2 i"r dpezp ( x,y ) dhpicxewa (ghy zcigil lwyna) d`ycna `ycd zetitv ztqe` `ycd zgqkny dgpda . 0 t 1 xy`k ( t,t 2 ) dleaxtd jxe`l `ycd z` gqkn mc` ?lelqnd seqa sq`i xy` `ycd lwyn edn ,zxaer `id oda zecewpa `ycd lk z` 2 libxz idze [0 ,u ] megza γ u ( t ) = ( t cos t,t sin t ) idi F ( x,y ) = sin( x 2 + y 2 ) x 2 + y 2 ( x,y ) :egiked lim u →∞ 1 u Z γ u -→ F · -→ dr = 0 .dneqg divwpet g xy`k g ( x 2 + y 2 ) dxevdn l`ivphet yi F - ly egiked :dkxcd 3 libxz :eayg Z γ ( x 2 y ) dx + (2 x + 1) y 2 dy . D = { ( x,y ) : | x | ≤ 1 , | y | ≤ 1 } xy`k iaeigd oeeika D megzd zty `ed

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Unformatted text preview: γ xy`k 4 libxz-nxt `id d`ad divfixhnxtdy egiked ." Strephoid " `xwp ' ( x,y ) : y 2 = 1-x 1+ x x 2 , x >-1 “ mewrd :znqeg `id eze` ghyd z` eayge mewrd i"r meqgd megzd ly divfixh ± 1-t 2 1 + t 2 , t 3-t 1 + t 2 ¶ , t ∈ [-1 , 1] 1 4 libxz miniiw ,xnelk .mirhw n- n akxend , a ≤ t ≤ b ,xeyina xebq ipebilet mewr γ ( t ) idi a = x < x 1 < ··· < x n-1 < x n = b . P k = γ ( x k ) onqp . γ ( a ) = γ ( b ) oke xyi ew `ed γ ( t ) ik miiwzn x i-1 ≤ t ≤ x i xeary jk . γ ( t ) ly (ziraihd divfixhnxtd) jxe` t"r divfixhnxtd z` yxetn ote`a enyx .1 . P k = (cos( 2 πk n ) , sin( 2 πk n )) gipp .2 .oixb htyn i"r zexiyi eayg ? γ mqeg eze` ghyd `edn (`) ? n → ∞ xy`k γ mqeg eze` ghyd ly leabd `ed dn (a) 2...
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