[BT Giai Tich] Dang 2- Khao Sat Tinh Kha Vi Tren R2

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<p>DNG VN QUANG ITSPIRITCLUB.NET []May 5, 2011 1 t nh gr adf ( Xo)co 2 ting hp: -Ting hp1 : n u Gr ad f ( Xo)k hng t n t i f khng kh vit iXo. -Ting hp2 : c Gr adf ( Xo)(c 40 % bit on )t hl m t i p bc 2. </p> <p>1 .Tm b i u t hc ca e( H) ( 2 0% ca b it on ), hm s e n uc p hic bi ut hc e( H) t ha: ( Xo+H) ( Xo)= ( Xo) E + E e( H)</p> <p>co E= 0 cio t co cun E &gt; 0 e( H)=]( Xc+H)-]( Xc)-uud]( Xc) HH 2 .Ki m ,xc nh n: l i mH0e( H)= 0ng oy soiNu ng thfk h vit iX0 Nu sait h fk hng k h vit iX0 Cu 1/ J( )= J( X)= ( x2+ y2) x|n1x2+y2X Gi i : R2\ { 0}:( phnny h uh tcc b igi ng n hau , ch k hc t ch l oihm ) // xt trng hp X thuc khong Ta c: t r ong k hon g R2\ { 0 } fl h m 2 bi n hp gi a hm hu t v hm lng gi c 1 : 2 cng l hm 2 bi n c mu u p dng q uit c : 1 : 2 l i nt c t r n R2\ { 0} p dng nh l : f kh vil i n t c t r n R2\ { 0 } v c vip hn t on ph nl : J( X)=]xJx +]yJy DNG VN QUANG ITSPIRITCLUB.NET []May 5, 2011 2 X=0 :// xt trng hp TiX=0 : Cho 1= x 0 c : ]( x,0)-]( 0,0)x=( x2+02) sn1x2+02x= x sin1x2 0 ki x 01( 0)= 0 Ch o 1= y 0 c : ]( 0,V)-]( 0,0)y= y sin1y2 0 ki y 02( 0)= 0 0roJ( 0)= 0</p> <p> J(X)J()= 0roJ(0) X + X e( X)</p> <p> e( X)= J(X) J() 0roJ(0) XX= J(X)X= X si n (1x2+ y2) X 1 CX 0 X 0 l i mX0e( X)= 0 hm s fk h v it i0 hmfkh vit r n R2 Cu 2/ J( )= J( X)=xy.x2+y2X Gi i : R2\ { 0} : // xt trng hp X thuc khong Ta c: t r ong k hon g R2\ { 0 } fl h m 2 bi n v t 1 : 2 cng l hm 2 bi nv t c mu u p dng q uit c : 1 : 2 l i nt c t r n R2\ { 0} p dng nh l : f kh vil i n t c t r n R2\ { 0 } v c vip hn t on ph nl : J( X)=]xJx +]yJy X=0 :// xt trng hp TiX=0 : Cho 1= x 0 c : ]( x,0)-]( 0,0)x= 0 0 ki x 0DNG VN QUANG ITSPIRITCLUB.NET []May 5, 2011 3 1( 0)= 0 Ch o 1= y 0 c : ]( 0,V)-]( 0,0)y= 0 0 ki y 0 2( 0)= 0 0roJ( 0)= 0</p> <p>Cho E = X X0= X( X0= 0) J(X)J()= 0roJ(0) X + X e( X)</p> <p> e( X)= J(X)J() 0roJ(0) XX= J(X)X=xy.x2+ y2XxyX2: tuc Jng 00 tx = X cos t y = X si n t e( X)=X.cos t X.sIntX2= cos t si n ttCho Xn= En= I1n,1n] 0l i mn+Xn= 0 e( X)=1n1n1n+1n=12 l i mX0e( X)=12</p> <p> l i mX0e( X)= 0 l soi Hm s k hng k h v it i 0</p> <p> hm s k hng k h vit r n R2 ( Tin o l 2 bi tp mn h l m mu cho 2 tin g hp k h v iv k hng k h v i ) cc bn lm theo sn bi trn) J( )= J( X)=x4x2+y2X k h v i )(A: J( )= J( X)= xy x2-y2x2+y2X k h v i )(A: Cc bn c t h t ham k ho v l m t h m mts bit p cc n gun k hc . (yllnu t i nm nh vi tbi, c g saistmong cc bngp l nsaumnh vi tthnhcnghn) Mit hc mc xi n l i n h :DngVnQuang y !m: her o_vq109 si t e: w w w .i t sp r i t cl ub.net </p>