; - (..) (..) . - .. .. .
{xn}, £ n0 , n>n0 |xn - a|< £.
{xn}, , £-
, . .
, .
n = 1/n, n = 1,2. .
, .
{Xn} = ∞
.
.
{Xn} , {1/Xn} 1/ → 0; {Xn} 0, {1/Xn} 1/→0→∞.
14.
.
.
f(x) g(x), x→R ( ) . ϵ ; f(x) ≤ g(x). limx→a f(x) = A, limx→a g(x) = B ≤.
.
{Xn}, ϵ , Xn ≠ , Xn→. f(Xn)→A, g(Xn)→B. n f(Xn)≤ g(Xn). , ≤.
16.
. .
( ) , , , .
, . ( ) ( ).
f(x), 0, 0, , ..
|
|
lim f(x) = f(X0) .
18.
, . .
. f(x) L x0, x, x0, f(x) L.
1) .
2) 2 .
2 .
3)
.
4) .
5) , .
. {xn}, , xn ≥ b (xn ≤ b), a a ≥ b (a ≤ b).
.
xn, , xn ≥ b. a ≥ b. , a < b. a - {xn}, ε = b - a N , n ≥ N |xn - a| < b - a. : -(b - a) < xn - a < b - a. , xn < b, . xn ≤ b . .
20.