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2 0.
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, e > 0 = [ ], n > | n | < e, ,
= .
2.) e, | n | < e, ..
| | = | | = < e,
4(4 n 2 + 5) > , n > .
= [ ], , n > | n | < e, .. .
. 1.) = [ ]; 2.) = [ ].
2. ) , n 2: . = = ,
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= = = = 0.
) n, :
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= = = =1.
) .
n! = 1 2 3 n,
(n + 1)! = 1 2 3 (n + 1),
,
(n + 1)! = n! (n + 1)
= = = .
, = .
. 2. ) ; 2. ) 0; 2. ) ; 2. ) 1; 2. ) 0.
3 0
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3. , :
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3 0.
1.) f (x) = 2 x 1, b = 3. , e d, e, d > 0, 0 < | x 2 | < d | f (x) 3 | < e.
e > 0
| f (x) 3 | = | (2 x 1) 3 | = 2 | x 2 |.
d £ , , 0 < | x 2 | < d,
| f (x) 3 | = 2 | x 2 |< 2 d £ 2 = e. , .
1.) e - . , d, e, d > 0, , 0 < | x 2 | < d,
| x 2 4 | < e.
| x 2|< d, | x +2|=| x 2+4| £ | x 2 | + 4 < d + 4 | x 2 4 | = | x 2 | | x + 2 |< d (d + 4).
|
|
| x 2 4 | < e , d (d + 4) = e d 2 + 4 d e =0,
d = 2 +
( , d ).
, e > 0 d > 0, 0 < | x 2 | < d
| x 2 4 | < e, ..
1.) e - . , d > 0, , 0 < | x + 1 | < d,
.
, d < 1.
| x + 1 | < 1
| x + 3 | = | x + 1 + 2 | > 2 | x + 1| > 2 1 = 1. .
, .
, d 1 .
, e > 0 d > 0,
0 < | x + 1 | < d .
, , .
. 1 ) d £ ; 1 ) d = 2 + d = min {1, }; 1) d = min {1, }.
2. ) , . , :
3 + 2 2 2 = ( 1) ( 2 + 3 + 2),
2 3 + 2 = ( 1) ( 2).
2. ) . , ( ).
= = = = .
2) . 2. = , .
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=
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= = = = 11=
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