flerdimlos081216

flerdimlos081216 - DEAÖGA AEA EÄAÖGA FEDEEAAY 86 Ö...

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Unformatted text preview: DEAÖGA AEA EÄAÖGA FEDEEAAY 86 Ö iaÒge ÐÒge×aÚ − x ≤ y ≤ x ≤ x ≤ 2 Ñ Ú iiÒ Øeg Öe Öa Öfö Ö×Ø i y Ðed fÖÚ i integraldisplayintegraldisplay D ( x + y ) dxdy = integraldisplay 2 parenleftbiggintegraldisplay x y = − x ( x + y ) parenrightbigg dx = integraldisplay 2 bracketleftbigg xy + y 2 2 bracketrightbigg x y = − x dx = integraldisplay 2 2 x 2 dx = bracketleftbigg 2 x 3 3 bracketrightbigg 2 = 16 3 . Úa Ö : 16 3 iha Ö braceleftbigg u = x + y v = x − y ⇔ braceleftbigg x = 1 2 ( u + v ) y = 1 2 ( u − v ) F ö ÖÚa Ö je f ( x,y ) ÒÒ ×eÒ fÙÒk Ø iÓÒ g ( u,v ) ×a ØØ f ( x,y ) = g ( u ( x,y ) ,v ( x,y )) ed je Öege ÐÒge Ö ∂f ∂x = ∂g ∂u ∂u ∂x + ∂g ∂v ∂v ∂x = ∂g ∂u + ∂g ∂v ∂f ∂y = ∂g ∂u ∂u ∂y + ∂g ∂v ∂v ∂y = ∂g ∂u − ∂g ∂v . Ò ×ØØÒ iÒgaÚd e××aÙ ØØÖÝk id ie ÖeÒ Ø ia ÐekÚa Ø iÓÒ ege Ö 2 ∂g ∂v = u 2 ⇔ g ( u,v ) = 1 2 u 2 v + φ ( u ) , d Ö φ ÖeÒgÓd ØÝk Ðig Ø C 1 fÙÒk Ø iÓÒaÚeÒÚa Ö iab e ÐD eÒa ÐÐÑ ÒÒa Ðö ×Ò iÒgeÒb ÐiÖa ÐÐØ× f ( x,y ) = 1 2 ( x + y ) 2 ( x − y ) + φ ( x + y ) . D y = x g ÐÐe Ö f ( x,x ) = φ (2 x ) ×d eÒ Ðö ×Ò iÒg×ÓÑ ÙÔÔ fÝ ÐÐe Ö f ( x,x ) = sin(2 x ) Ö f ( x,y ) = 1 2 ( x + y ) 2 ( x − y ) + sin( x + y ) . Úa Ö : A ÐÐÑ Ò Ðö ×Ò iÒg f ( x,y ) = 1 2 ( x + y ) 2 ( x − y )+ φ ( x + y ) . D eÒ Ðö ×Ò iÒg ×ÓÑ ÙÔÔ fÝ ÐÐe Ö f ( x,x ) = sin 2 x Ö f ( x,y ) = 1 2 ( x + y ) 2 ( x − y ) + sin( x + y ) . a ØØ F ( x,y,z ) = x 2 + y 2 − ( z + 1) 2 D ÖkÓÒ eÒÒ iÚÝ ØaÒ F ( x,y,z ) = 0 Ñ P : ( a,b,c ) ÖeÒ ÔÙÒk ØÔkÓÒ eÒd Ö grad F ( a,b,c ) negationslash = ×ge×eÒ ekÚa Ø iÓÒ fö ÖØaÒgeÒ ØÔ ÐaÒ e Ø i P aÚ grad F ( a,b,c ) · ( x − a,y − b,z − c ) = 0 . E fØe Ö×ÓÑ grad F = (2 x, 2 y, − 2( z + 1)) b ÐiÖ grad F (3 , 4 , − 6) = (6 , 8 , 10) = 2(3 , 4 , 5) Óh eÒ ekÚa Ø iÓÒ fö ÖØaÒgeÒ ØÔ ÐaÒ e ØÖ 3( x − 3) + 4( y − 4) + 5( z + 6) = 0 ⇔ 3 x + 4 y + 5 z + 5 = 0 ....
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flerdimlos081216 - DEAÖGA AEA EÄAÖGA FEDEEAAY 86 Ö...

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