Infi2_hw9 - 9 oeilib -2007 aia` - (104281) 2 itpi` dpigad...

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Unformatted text preview: 9 oeilib -2007 aia` - (104281) 2 itpi` dpigad ixg` dry , 18 . 9 . 2007 ,iyily mei :dybd jix`z .dpigad xcga mb dceard z` yibdl ozip .` cren ly jix`zd `ed dybdd jix`z :dxrd ,oey`x mei cr dceard z` yibdl jixv qxewd wcea ici lr wcaiz ezceary dvexy in . 12 : 30 dry , 2 . 9 . 2007 : α xhnxta dielzd d`ad divwpetd dpezp .1 f ( x,y ) = yx α + xy α x 2 + y 2 ( x,y ) 6 = (0 , 0) ( x,y ) = (0 , 0) , (2 , 3) oeeikl ziy`xa zpeekn zxfbp zlra ,dtivx divwpetd α ikxr el`l e`vn .dxifbe z` eayg :fnx . a 6 = 0 xear I ( a ) = Z 1 dx ( x 2 + a 2 ) 3 :`ad lxbhpi`d z` eayg .2 . F ( a ) ly dipyd zxfbpl I ( a ) oia xyw e`vne F ( a ) = Z 1 dx x 2 + a 2 lxbhpi`d :mi`ad mitirqd z` egiked .3 . x lkl Z x e- t 2 dt 2 + Z 1 e- x 2 ( t 2 +1) t 2 + 1 dt = π 4 (`) . x itl l`ny sb` z` exfib :fnx lim x →∞ Z 1 e- x 2 ( t 2 +1) t 2 + 1 dt = 0 (a) Z ∞ e- t 2 dt = √ π 2 (b) :xicbp .xeyina ziliaxbhpi` divwpet f ( x,y ) idz .4 F ( x,y ) = Z x Z y f ( s,t ) dtds .dtivx F ( x,y )- y e`xd (`)- y e`xd .dtivx- y e`xd ....
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Infi2_hw9 - 9 oeilib -2007 aia` - (104281) 2 itpi` dpigad...

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