Lesson_7

# Lesson_7 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 7 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 7 lebxz weipitiv ilhp :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd 1 dxcbd leabd m` x dcewpa dxifb f-y mixne` . x dcewpd ly daiaqa zxcbend divwpet f idz f ( x ) = lim h → f ( x + h )- f ( x ) h .(iteq) miiw :zexfbp ly dwihnzix` illk if` ,reaw `ed a-e , x-a zexifb zeivwpet izy od f, g m` ( af ) ( x ) = af ( x ) (1) ( f ± g ) ( x ) = f ( x ) ± g ( x ) (2) ( f · g ) ( x ) = f ( x ) · g ( x ) + f ( x ) · g ( x ) (3) . f g ( x ) = f ( x ) · g ( x )- f ( x ) · g ( x ) g 2 ( x ) , g ( x ) 6 = 0 m` (4) :zxyxyd llk f ( x )-a dxifb g m`e x dcewpa dxifb f m` . Φ = g ◦ f idz :miiwzne x-a dxifb Φ = g ◦ f f` Φ ( x ) = ( g ◦ f ) ( x ) = g ( f ( x )) · f ( x ) (5) .zxyxyd llk z`xwp ef dxifb zgqep 1 . f ( x ) = x + ( x- 1) arcsin r x x + 1 xy`k f (1) e`vn 1 libxz :oexzt lawp zxfbpd zxcbd itl f (1) = lim h → f (1 + h )- f (1) h = lim h → (1 + h ) + (1 + h- 1) arcsin r 1 + h 1 + h + 1- 1 h = lim h → h 1 + arcsin r 1 + h 2 + h ! h = 1 + arcsin √ 2 2 = 1 + π 4 .zxfbpd z` eayge ,zexifb ze`ad zeivwpetd zecewp el`a ewca 2 libxz (`) f ( x ) =      x 2 sin 1 x x 6 = 0 x = 0 :oexzt zxyxyd llke zexfbp ly dwihnzix` illk itl f` , x 6 = 0 m` • f ( x ) = 2 x · sin 1 x + x 2 · cos 1 x ·- 1 x 2 = 2 x sin 1 x- cos 1 x zxfbpd zxcbda ynzydl miaiig , x = 0 m` • f (0)...
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## This note was uploaded on 03/12/2011 for the course MATH 104010 taught by Professor Dr.miriambarazinna during the Winter '11 term at Technion.

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Lesson_7 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 7 lebxz...

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