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Chapter 2 Section 5

# Chapter 2 Section 5 - substitution ∞-∞ ⋅ ∞ ∞ ∞...

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Chapter 2 Section 5 Evaluating limits algebraicly 1

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The rule of substitution only works when f(x) is continuous. ( 29 ( 29 10 5 x lim   gives   on, substituti   by   which, 5 x lim 5 x 5) 5)(x (x lim 5 x 25 x lim write   can   we   5   to   equal   not   but   5,   to   close   x for    is   limit   the   , definition   by   Since, 5 x 5 x 5) 5)(x (x 5 x 25 x   but, form   ate indetermin   the   called   is    which    0 0    gives   on substituti 5 x 25 x lim Consider 5 x 5 x 5 x 2 5 x 2 2 5 x = + + = - + - = - - + = - + - = - - - - 2
The indeterminate forms are When f is indeterminate at x = c, we try to transform f into a new expression that coincides with f(x) near c but is continuous at x = c and use

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Unformatted text preview: substitution. ∞-∞ ⋅ ∞ ∞ ∞ and , , , 3 4 9 ) 2 ( lim . 12 # , 98 2 4--+ → h h h page h 4 16 4 lim . 16 # 98 page 16--→ x x x 5 +-+ → x x x x 2 1 1 lim . 26 # 98, page 6 ( 29 ) tan( ) sec( lim . 30 # 98, page 2 θ π-→ 7 1 3 1 3 lim . 32 # 98, page 2--→ x x x 8 a x x a x page a x--+ → 2 2 4 ) ( lim . 48 # , 98 9 4 4 lim : 4 + +-→ x x Example x 10...
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Chapter 2 Section 5 - substitution ∞-∞ ⋅ ∞ ∞ ∞...

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