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Приклад 1. Знайти границі:

a) lim → ; б) lim → ; в) lim → ;
( ) ( )
г) lim → ; д) lim → / ; е) lim → ;

( ) ( )
( )
a) lim → = = lim → =
( )

∗ /( )
= lim → = -2; б) lim → = =
/
( ) ( )
lim → = = lim → =

( )

= lim → = lim → = = ∗ 1 = ;

( )
в) lim → = = lim → ( ) =

( )
lim → ∗ = = lim → ( ) =

=lim → ∗ = ; г) lim → ( ) = =

( ) /
= lim → ( ( )) = lim → ( /( ))∗ = lim → =

/
= = lim = ; д) lim → / = =
→

( ) ( / )∗
= lim → / ( ) = lim → / ( / )∗ = lim → / =

( ) ∗
= = *(lim → / ) = *(lim ) =
( ) → ∗
∗
= *(lim ) = *(lim ) =
→ → ∗

= ∗ lim = ∗ = ;
→
( ) ( )
е) lim → = = lim → cos( ) ∗

( )
( ( )) / ( )
*lim → = (−1) ∗ lim → =

( ( )) ( / ))∗
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