Lesson_6 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 6 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 6 lebxz weipitiv ilhp :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd ,q`xhyxiiee ihtyn) rhwa zetivx ,zetivx i` zecewp beeiq ,dcewpa zetivx (miipiad jxr htyn 1 dxcbd . lim x → x f ( x ) = f ( x ) m` x-a dtivx z`xwp , x ly daiaqa zxcbend , f ( x ) divwpet . | f ( x )- f ( x ) | < f` | x- x | < δ m`y jk δ > yi ε > lkl : ε- δ oeyla dxcbdd . f ( x n ) → f ( x ) mb x n → x dxcq lkl :zexcq oeyla dxcbdd 2 dxcbd ,dwilq zetivx-i` zcewp z`xwp x dcewpd . x ly daiaqa zxcbend ,divwpet f ( x ) idz miiwnd L iynn xtqn miiw m` lim x → x f ( x ) = L . f ( x ) 6 = L e` ,xcben `l f ( x ) j` 3 dxcbd miniiw m` dvitw zcewp z`xwp x dcewpd . x ly daiaqa zxcbend ,divwpet f ( x ) idz mxeary L 2-e L 1 mipey miiynn mixtqn ipy lim x → x- f ( x ) = L 1 lim x → x + f ( x ) = L 2 1 4 dxcbd .zixwir zetivx-i` zcewp z`xwp dvitw dpi`e dwilq dpi`y zetivx-i` zcewp lk f ( x ) = 1 x f ( x ) = sin 1 x 2 1 libxz .`l e` x dcewpa dtivx divwpetd m`d eraw libxzd ly mitirqdn cg` lka .dze` ebeeq - zetivx-i` ly dxwna (`) f ( x ) = x · sin 1 x x 6 = 0 x = 0 x = 0 , x 6 = 0 :oexzt .zetivx zeivwpet ly dakxde dltknk x a dtivx dpid f ( x ) = x · sin 1 x f` x 6 = 0 m` ik ,'uieecpqd llk itl lim x → x f ( x ) = lim x → x · sin 1 x = 0 f` x = 0 m` ≤ x · sin 1 x = | x | · sin 1 x ≤ | x | ---→ x → . x = 0 a mb dtivx dpid f ( x ) okle (a) f ( x ) = cos πx 2 | x | ≤ 1 | x- 1 | | x | > 1 x = ± 1 :oexzt :zyxetn dxeva divwpetd z` meyxp f ( x ) = cos πx 2 | x | ≤ 1 | x- 1 | | x | > 1 = - ( x- 1) x <- 1 cos πx 2- 1 ≤ x ≤ 1 ( x- 1) x > 1 :lawp x = 1 xear f` lim x → 1- f ( x ) = lim x → 1- cos πx 2 = cos π 2 = 0...
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Lesson_6 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 6 lebxz...

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