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Lesson_3

# Lesson_3 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 3 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 3 lebxz oxia xnr :dkixr cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd zeivwpet ly zeleab x → a xy`k iteq leab (`) 1 dxcbd ( * ) < | x- a | < δ miiwnd x lkly jk δ > yi ε > lkl m` , lim x → a f ( x ) = L ik xn`p . | f ( x )- L | < ε miiwzn .( ( * ) ly zernynd z` xiaqdl :lbxznl ) :dygnd . x = 5-a iteq leab yi . f ( x ) = 2 5 x (1 . x = 0-a iteq leab oi` . f ( x ) = 1 | x | (2 . x = 0 ly daiaq likn epi` | f ( x )- L | < 1 miiwzn eay xef`d 1 . lim x → 1 (2 x + 1) = 3 ik dxcbd i"tr gikep 1 libxz . ε > `di :dgked . | 2 x + 1- 3 | < ε miiwzn < | x- 1 | < δ miiwnd x lkly jk δ > yi :l"v | 2 x + 1- 3 | = | 2 x- 2 | = | 2( x- 1) | = 2 | x- 1 | ? < ε ⇐⇒ | x- 1 | < ε 2 .l"yn . δ = ε 2 xgap okl . lim x → x + 1 x- 1 =- 1 ik dxcbd i"tr gikep 2 libxz . ε > `di :dgked . x + 1 x- 1- (- 1) < ε miiwzn < | x- | < δ miiwnd x lkly jk δ > yi :l"v x + 1 x- 1- (- 1) = x + 1 x- 1 + 1 = x + 1 + x- 1 x- 1 = 2 x x- 1 = 2 | x | | x- 1 | . | x- 1 | > 1 2 ,jkitle x- 1 <- 1 2 ,okle x < 1 2 f` | x | < 1 2 m` . 2 | x | | x- 1 | < 2 | x | 1 2 = 4 | x | ( * ) < ε miiwzn | x | < 1 2 xear ,zrk . | x | < ε 4 xear miiwzn ( * ) .l"yn . δ = min ε 4 , 1 2 xgap okl ? x → xy`k f ( x ) divwpetd ly leabd miiw b ikxr eli` xear 3 libxz f ( x ) = x + 1 x 6 = 0 b x = 0 :oexzt miiwnd x xear f ( x ) ly mikxra mipiiprzn ep` dxcbdd itl ik , b lkl miiw leabd .leabd lr rityn `l x = 0 xear f ( x ) ly jxrd xnelk , < | x- | < δ : b > 1 xear ,lynl 2 zeleab ly dwihnzix` (a) ( .jynda gkei ik oiivle zernyn xiaqdl ,dzika gked `l oiicr m` :lbxznl ) f` . g ( x )---→...
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