Lesson_6

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 6 lebxz weipitiv ilhp :dkixr oxia xnr ,cwy inrp x&amp;quot;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 ) | &amp;lt; f` | x- x | &amp;lt; δ m`y jk δ &amp;gt; yi ε &amp;gt; 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 | &amp;gt; 1 x = ± 1 :oexzt :zyxetn dxeva divwpetd z` meyxp f ( x ) = cos πx 2 | x | ≤ 1 | x- 1 | | x | &amp;gt; 1 = - ( x- 1) x &amp;lt;- 1 cos πx 2- 1 ≤ x ≤ 1 ( x- 1) x &amp;gt; 1 :lawp x = 1 xear f` lim x → 1- f ( x ) = lim x → 1- cos πx 2 = cos π 2 = 0...
View Full Document

## 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.

### Page1 / 8

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online