infi2HW10 - yi f ( x,y ) = xy divwpetl ,lynl ;divwpetd...

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10 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2008 uxnl 27 :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 : L `ed ( a,b ) - a f ( x,y ) ly leabdy jkl lewy `ad i`pzdy egiked θ lkl `ad oeieeiyd i` miiwzn 0 < r < R lekly jk ϕ ( r ) ziynn divwpet zniiwe R > 0 miiw | f ( a + r cos θ,b + r sin θ ) - L | < ϕ ( r ) oke lim r 0 + ϕ ( r ) = 0 2 libxz :miniiw `l mdy gikedl e` mi`ad zeleabd z` aygl lim ( x,y ) (0 , 0) ( | x | + | y | ) - ( x + y ) 2 .1 lim ( x,y ) (1 , 1) xy - x - y + 1 p x 2 + y 2 - 2 x - 2 y + 2 .2 lim ( x,y ) (0 , 0) x 2 y x 4 + y 2 .3 .miiw leabd m`d iynn α jxr lk xear ewca - lim ( x,y ) (0 , 0) xy α log(1 + x 2 + y 2 ) .4 3 libxz mz`y e`cee .dxcbdd megz lka zetivx ody egikede ze`ad zeivwpetd ly daebd ieew z` exiiv
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Unformatted text preview: yi f ( x,y ) = xy divwpetl ,lynl ;divwpetd dxicbn eze` ghynd z` (&quot;ze`xl&quot;) oiincl mileki ?z`f mi`ex mz` m`d ,ziy`xa &quot;ske`&quot; f ( x,y ) = x + y .1 f ( x,y ) = xy .2 y 6 = 0 xy`k , f ( x,y ) = x y .3 f ( x,y ) = x .4 f ( x,y ) = max { x,y } .5 1 4 libxz xicbpe dpezp dtivx divwpet f : R 2 → R `dz g ( x,y ) = Z y f ( x,t ) dt. . R 2 a dcewp lka dtivx `idy egikede ,ahid zxcben g dnl exiaqd 5 libxz :zniiwnd divwpet f ( x,y ) idze dtivx divwpet g ( x,y ) idz . x,y lkl f ( x,y ) = f ( y,x ) .` . f ( x,y ) = g ( x,y ) miiwzn y ≥ x lkl .a .dtivx f ( x,y ) y egiked 2...
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infi2HW10 - yi f ( x,y ) = xy divwpetl ,lynl ;divwpetd...

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