infi2HW9

# infi2HW9 - 9 A4'qn milibxz oeilb 104281 2 itpi`:dybd...

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Unformatted text preview: 9 A4 'qn milibxz oeilb - 104281 7/7/2006 - 2 itpi` :dybd jix`z .(ef dryl jenq sq`p libxzd !xg`l `l `p) mixdva 12 : 00 dry cr -- 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"z xtqn z`e cinlzd my : 1 libxz :divxbhpi` xcq etilgd 1 -1 1 0 0 1 x2 1-x2 f (x, y)dy dx f (x, y)dx dy : .1 .2 2 libxz :mi`ad milxbhpi`d z` eayg i"r meqgd megzd `ed . D (x + y)3 (x - y)3 dxdy D x + y = 1; x + y = 3; x - y = 1; x - y = -1; xy`k , .1 D= 2 {(x, y)| x2 a + . y2 b2 1} xy`k , D 1- x2 a2 + y2 b2 1 2 1 2 dxdy .2 x = au, y = bv :mipzynd selig z` eqp :fnx :zeleaxtd i"r meqgd megzd `ed . x sin(xy) D dxdy y D y 2 = 2 x; y 2 = x; x2 = y; x2 = 2y; xy`k , xy`k , 2 .3 i"r meqgd megzd `ed . D xy dxdy D xy = 2; xy = 3x; y = 1 x2 ; y = 2x2 ; 2 : .4 3 libxz :( 0<c<d - e 0<a<b ) dveawd ghy z` eayg A = {(x, y) R2 | x > 0, y > 0, ay x3 by, cx y 3 dx} : 4 libxz :ieewd lxbhpi`d z` eayg (x2 - y)dx + (y 2 + x)dy C :jxc mixaere (1, 2) -a miniizqne (0, 1) -a miligznd C minewrd xear 1 .zecewpd oia xagnd xyid .1 . (1, 2) - l (1, 1) - ne , (1, 1) . -l (0, 1) - n mixyid mieewd .2 (t, t2 + 1), 0 t 1 dleaxtd .3 : 5 libxz eayg (0, 0) - n y = x3 ly sxbd jxe`l f (x, y) = 4 |xy| xear C f (x, y)dS ieewd lxbhpi`d z` . (1, 1) cre : :`ed 6 libxz .1 C 1 2 i"r meqgd ghydy e`xd .xebqe heyt mewr C idi xdy - ydx C ?ef dxevl mi`xew ji`) . (a cos , b sin ), 0 2 mewrd i"r meqgd ghyd z` e`vn .2 .(!dpekpd d`vezd z` mzlaiwy ewca : 7 libxz :ieewd lxbhpi`d z` eayg (6xy 2 - y 3 )dx + (6x2 y - 3xy 2 )dy C . (1 + 2 sin t, 4 - 2 cos2 t), 0 t 2 lelqnd xear .gep lelqn exgae lelqna zelz oi` ik e`xd :fnx 2 ...
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## This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Spring '08 term at Technion.

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infi2HW9 - 9 A4'qn milibxz oeilb 104281 2 itpi`:dybd...

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