. f(x) ¥, e>0 >0, , ïï>M
, f(x) .
:
:
y y
A A
0 0
x x
y y
A A
0 0
x x
>M
<M.
1. , = const.
, f(x) g(x) .
2.
.
3.
.
4.
5. f(x)>0 = , >0.
f(x) < 0, f(x) ³ 0, f(x) £ 0.
6. g(x) £ f(x) £ u(x) = , .
.
tg5x ~ 5x sin7x ~ 7x 0, , , :
. .
1 cosx = 0, .
.
a b - , b - , a, g = a + b - , a. .
, a - g.
. 2 + 0, . , a = 2, b = ,
.
, P(x) = a0xn + a1xn-1 ++an,
Q(x) = b0xm + b1xm-1 ++bm - .
:
, .
, , :
. .
. .
. .
. .
. .
. .
.
x2 6x + 8 = 0; x2 8x + 12 = 0;
D = 36 32 = 4; D = 64 48 = 16;
x1 = (6 + 2)/2 = 4; x1 = (8 + 4)/2 = 6;
x2 = (6 2)/2 = 2; x2 = (8 4)/2 = 2;
. .
: =
= .
. .
|
|
. .
.
x2 3x + 2 = (x 1)(x 2)
x3 6x2 + 11x 6 = (x 1)(x 2)(x 3), ..
x3 6x2 + 11x 6 x - 1
x3 x2 x2 5x + 6
- 5x2 + 11x
- 5x2 + 5x
6x - 6
6x - 6 0
x2 5x + 6 = (x 2)(x 3)
. .
- , .. 2 -∞ +∞.
. z , a b , i , :
a z (a = Re z), b - (b = Im z).
a =Re z =0, z , b = Im z = 0, z .