. , , .
F(x) A X0, F(x), A X0, F(x) A.
, ,
{xn} {yn} , a b, :
) {xnyn} a b, . .
lim[n―∞](XnYn)=lim[n―∞]Xnlim[n―∞]Yn=ab
.
) {xn yn} ab, . .
lim[n―∞](Xn*Yn)=lim[n―∞]Xn*lim[n―∞]Yn=a*b
.
lim[n―∞]KXn=K lim[n―∞]Xn
k.
) {Xn/Yn} a/b, . .
lim[n―∞](Xn/Yn)=lim[n―∞]Xn/lim[n―∞]Yn=a/b
, Yn limYn=b!=0.
, .
, U(x0)
f(x0 + h) = f(x0) + Ah + o(h)
A .
x0, U(x0)
fL f x0. .
s = s(t) . v(t0) = s'(t0) t0. a(t0) = s''(t0) t0.
y = f(x) x0 x0, , y = f(x).
f(x) = x2.
f(x) = | x |.
f'(x0) = sgn x0,
sgn . x0 = 0, f'(x0) .
1. y = f(x) (a, b). f (a, b).
x (a,b).
, x0 α = α(Δx), dX->0 ,
|
|
, , f x = x0. x0 , f (a, b).
.
, .
(a, b) (a, b). , , x = 0. , (1) Δx. , x = 0 Δx > 0, Δy = Δx, Δx < 0, Δy = − Δx.
, x = 0.
, , .
1) (uv)=uv,
2) (uv)=uv+vu,
3) (v/u)'=(uv-uv)/u^2