. A f (x) a, a , , a, ε > 0 δ > 0 , x, | x a | < δ, x ≠ a, | f (x) A | < ε.
. A f (x) a, a , , a, , a, A.
f (x) a, .
A 1 f (x) a, ε > 0 δ > 0 ,
A 2 f (x) a, ε > 0 δ > 0 ,
a. . x → 0 : . ,
ε > 0 δ- a, x, | x a | < δ, x ≠ a, | f (x)| > ε, , f (x) a :
, x = 0 , +∞ ∞. ,
ε > 0 δ > 0, x > δ | f (x) A | < ε, , f (x) x, , A:
x, : :
, , ε > 0 δ > 0, x > δ f (x) > ε. , ε > 0 δ > 0, x > δ f (x) < ε. , ε > 0 δ > 0, x < δ f (x) < ε.
f (x) a, a, f (, a ). , A ≠ 0, a, ( , a) f , A.
δ > 0, x, δ- a,
|
|
g (x) ≤ f (x) ≤ h (x), |
, |
δ > 0, x, δ- a,
f (x) < g (x), |
A ≤ B.
f (x) g (x) a,
,
B ≠ 0 g (x) ≠ 0 δ- a.
f (x) a g (y) f (a) g (f (x)) a.
:
( a > 0, a ≠ 1):
|
.
α (x) x → a ( a ∞), x = 0 . ( ) .
x → a .
x → a a x → a .
a f (x), g (x), h (x) , f (x) = g (x) h (x), , f (x) g (x) x → a:
f (x) ~ g (x). |
, x → 0, 1 x → 0. x → 0:
sin x ~ x tg x ~ x arcsin x ~ x arctg x ~ x ex 1 ~ x ln (1 + x) ~ x (1 + x)α 1 ~ α x. |
.
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. f (x) g (x) , , , , , .
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(4)
. (2) (3) .
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2. , ..
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f(u) ,
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a f (x)
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