y=f(x) x→a x →∞, , .. , .
.
- f(x) =(x -1)2 x →1, (. .).
- f(x) = tg x x →0.
- f(x) = ln (1+ x) x →0.
- f(x) = 1/ x x →∞.
:
. y=f(x) x→a b α(x): f (x)=b+ α(x) .
, , f (x)=b+α(x), a(x) x→a.
.
- . f(x)=b+α(x) |f(x) b|=| α|. a(x) , ε δ a, x , a(x) |α(x)|< ε. |f(x) b|< ε. , .
- , ε >0 δ a |f(x) b|< ε. f(x) b= α, |α(x)|< ε, , a .
3. :
1) , .
2) , .
3) , .
- , - . , f(x), 0, . , x0, > 0 δ = δ () > 0, ≠ 0 , | - 0 | < δ, |f(x)| > M. :
.,
, > 0 δ = δ (M) > 0, z < - δ f(x) > M. . . . , . . f(x) . . ., ψ () = 1/f(x) .
f(x) 0 .
f(x) 0,
1. 0
2.
3. 0.
, =f(x) , ,
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