1. . . n an , .. {an} a1, a2an. 1, 2 .., - ...
2. . y=f(x), →∞, , (/>0), , ││> │F(x)-A│>E.
3. y=f(x), →0( 0), . δ, , , 0, , │-0│>δ │F(x)-A│<.
4. 1. y=α(x) x→x0
( x → ∞), .
2. f (x) x → a , , A α (x) x → a
F(x)=A+α(x).
. ;
( .) ;
, 0 .
6. y=F(x) x→x0( x → ∞), , . M, . δ ( M), ≠0 │-0│<δ │F(x)│>.
-: 1. , 0 ;
.;
3. , 0 ..
7. α (x) , →0 →∞ α()≠0, - →0 →∞.
f(x)-, →0 →∞, α()= - →0 →∞.
8. . .
. , .. lim(f(x)+q(x))=A+B, (→0 →∞)
, .. lim(f(x)*q(x))=A+B (x→x0 →0).
, .. lim C*f(x)=C*A,(-const, →0 →∞)
, , 0, .. lim = (≠0) (→0 →∞).
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. lim f(u)=A (u→u0), limϕ(x)=U0(x→x0), : limf(ϕ(x))=A(x→x0).
0 f(x)<q(x), limf(x)≤limq(x) (→0 →∞).
9. 1- . : lim =1(x→0)
10. e . : lim(1+ )n=e (n→∞)
11. y=f(x) 0, :1. 0, .. f(x); 2. 0, .. . f(x), →0; 3. , .. lim f(x)=f(x0), (x→x0).
12. - . 1. F(x) q(x) x0, f(x)q(x); f(x)*q(x); (q(x0)≠0) x0 2. f(x) 0 f(x0)>0, 0, f(x)>0. f(x0)<0 . 3. y=f(u) 0 =ϕ() 0, =f(ϕ(x)) 0.
13. - . . 1. y=f(x) [;], , .. . , [;], f(x)≤M. 2. =f(x) .[a;b], m M. 3. =f(x) [a;b] , Ѫ(;), f(c)=0.
14. . =f(x) 0 . , →0, ,.. ,=lim (x→0) f/=lim (∆x→0)
. : S(t)- , v t v(t)=S/(t)
: x0 y = f(x) . K=f/(x0).
15. . 0 , 0,