infi2_moed_b

infi2_moed_b - 8.10.2006 ,104281 ,2 'itpi`a dpiga 'a cren...

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Unformatted text preview: 8.10.2006 ,104281 ,2 'itpi`a dpiga 'a cren ,e"qyz aia` .ivge zery yely `ed dpigad jyn .ze`ad zel`yd yy lr dpr daeyz :mkizeaeyz z` ewnp .xfr xneg lka ynzydl oi` .lawzz `l zwnepn `l .1 dl`y . lim x → 0+ log(1 + x ) x leabd z` ayg .` (5) :lhitel i"r .oexzt lim x → 0+ log(1 + x ) x = lim x → 0+ 1 1+ x 1 = 1 lxbhpi`d α ikxr eli` xear reawl ick '` sirqa ynzyd .a (10) llkend Z 1 dx [log(1 + x )] α .xcazn `ed α ikxr eli` xeare ,qpkzn .qt` zaiaqa wx meqg eppi` f α ( x ) = 1 [log(1+ x )] α cpxbhpi`d .oexzt meqg eppi` `ed mby g α ( x ) = 1 x α cpxbhpi` mr d`eeyd ogan rvap :mcew sirqa ynzype qt` zaiaqa lim x → 0+ f α ( x ) g α ( x ) = lim x → 0+ log(1 + x ) x α = 1 α = 1 1 miqpkzn R 1 g α ( x ) dx- e R 1 f α ( x ) dx milxbhpi`d dfd aeyigd t"r okle α < 1 m"m` qpkzn R 1 g α ( x ) dx lxbhpi`d ;cgia mixcazne . α < 1 m"m` qpkzn R 1 f α ( x ) dx .2 dl`y i"r zxcben f ( x, y ) idz .f ( x, y ) = x 2 y +2 y 2 (2 x 2 + y 2 ) α ( x, y ) 6 = (0 , 0) ( x, y ) = (0 , 0) ? (0 , 0) :a dtivx f divwpetd α ikxr eli` xear .`(5) :zeivwpet izy ly mekqk f ( x, y ) divwpetd z` meyxp .oexzt x 2 y + 2 y 2 (2 x 2 + y 2 ) α = x 2 y (2 x 2 + y 2 ) α | {z } g α ( x,y ) + 2 y 2 (2 x 2 + y 2 ) α | {z } h α ( x,y ) z` `vnp .ziy`xa qt` zeidl zexcben h α ( x, y )-e g α ( x, y ) xy`k-eqd d`vezd ,dtivx didz el` zeivwpetn zg` lky jkl mi`pzd dtivx ef dtivx qelt dtivx ,xekfk) mi`pzd jezig i"r lawzz zit-da zeivwpetd z` meyxp .(dtivx-i` `id dtivx-i` qelt dtivxe :zix`let dbv g α ( r ; θ ) = r 3 cos 2 θ sin θ (2 r 2 cos 2 θ + r 2 sin 2 θ ) α = r (3- 2 α ) · cos 2 θ sin θ 1 + cos 2 θ | {z } meqg ote` eze`a .dtivx g α ( x, y ) ik miiwzn α < 3 2 xy`ky raep o`kn :d`ad dbvdd t"r ,dtivx h α ( x, y ) ik miiwzn α < 1 xy`k h α...
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infi2_moed_b - 8.10.2006 ,104281 ,2 'itpi`a dpiga 'a cren...

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