infi2HW4

# infi2HW4 - 4 'qn milibxz oeilb - 104281- 2 itpi` .(ef dryl...

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Unformatted text preview: 4 'qn milibxz oeilb - 104281- 2 itpi` .(ef dryl jenq sq`p libxzd !xg`l `l `p) mixdva 12 : 00 dry cr -- 4 / 2 / 2006 :dybd jix`z A 4 lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz z` xexiaa oiivl `p .micigia dybdd .(!zekiq wcdna) wcedn yibdl `p .mixqlw e` zeiwy `ll .xry sca jxev oi` .f&quot;z xtqn z`e cinlzd my : 1 libxz :ik egiked . ( a,b ) zaiaqa dneqgd mipzyn ipya divwpet f ( x,y ) idz lim ( x,y ) → ( a,b ) f ( x,y ) = L :miiwzn ( a,b ) dcewpd ly idy lk daiaqay jk φ ( r ) divwpet zniiw m` wxe m` | f ( a + r cos θ,b + r sin θ )- L | ≤ φ ( r ) :exicbd :&quot;m` wxe&quot;-d oeeikl fnx . lim r → + φ ( r ) = 0 oke φ ( r ) = sup θ | f ( a + r cos θ,b + r sin θ )- L | : 2 libxz .ozip m` leabd z` eayge miniiw mi`ad zeleabd m` ewca lim ( x,y ) → (0 , 0) √ x 2 y 2 +1- 1 x 2 + y 2 + xy .1 lim ( x,y ) → (0 , 1) 1- cos 2 xy x 2 y sin( πy ) .2 lim ( x,y ) → (1 , 2) ( x + y- 3) 2 √ x 2 + y 2- 2 x- 4 y +5 .3 lim ( x,y ) → (0 , 0) x 2- x + y 2- y | x | +...
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## This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Winter '08 term at Technion.

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infi2HW4 - 4 'qn milibxz oeilb - 104281- 2 itpi` .(ef dryl...

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