.
.
:
y1 = a11x1 + a12x2
y2 = a12x1 + a22x2
1 2 .
,
(1, 2) = 11 + 22.
, 1 2 .
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.
1 2 . :
.
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.
.
(1, 2) = 27 .
: 11 = 27, 12 = 5, 22 = 3.
: ;
(27 - l)(3 - l) 25 = 0
l2 - 30l + 56 = 0
l1 = 2; l2 = 28;
. :
17x2 + 12xy + 8y2 20 = 0.
11 = 17, 12 = 6, 22 = 8. =
:
(17 - l)(8 - l) - 36 = 0
136 - 8l - 17l + l2 36 = 0
l2 - 25l + 100 = 0
l1 = 5, l2 = 20.
: - .
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: :
, l1 = 2, l2 = 6.
:
m1 = 1, n1 =
m2 = 1, n2 =
:
.
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, l1 = 1, l2 = 11.
:
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m1 = 1, n1 =
m2 = 1, n2 =
:
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:
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4 + 32 + 16 = 0
: a11 = 0; a12 = 2; a22 = 3.
:
: l1 = -1, l2 = 4.
l1 = -1 l2 = 4
m1 = 1; n1 = -0,5; m2 = 1; n2 = 2;
= (1; -0,5) = (1; 2)
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:
1) m: m{xn} = {mxn}, .. mx1, mx2,
2) () : {xn} {yn} = {xn yn}.
3) : {xn}×{yn} = {xn×yn}.
4) : {yn} ¹ 0.
.
. {xn} , >0, n :
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xn £ M.
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: lim xn = a.
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xn a; xn b; a ¹ b.
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{xn} = n .
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1 £ 2 £ 3 £ £ n £ xn+1 £
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xn > a - e.
a - e < xn < a + e
-e < xn a < e ôxn - aô< e, .. lim xn = a.
.
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{xn} = .
{xn} , .
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, n : xn < 3.
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, £ 3. {xn} , , :
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, 2,5 3. , .
, 2,71828
, , :
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y = lnx.
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= 10, lnx = ln10y, lnx = yln10
= , = 1/ln10 0,43429- .
.
y f(x)
A + e
A
A - e
0 a - D a a + D x
f(x) = (.. = )
. f(x) , e>0 D>0, ,
0 < ïx - aï < D
ïf(x) - Aï< e.
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- D < x < a + D, x ¹ a, - e < f(x) < A + e.
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. f(x) A1 x < a, - f(x) = , f(x) A2 x > a, f(x) = .
f(x)
2
1
0 a x
, f(x) = , .
1 2 f(x) = . , f(x).
.
. f(x) ¥, e>0 >0, , ïï>M
, f(x) .
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:
y y
A A
0 0
x x
y y
A A
0 0
x x
>M
<M.
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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) = , .
. f(x) = , >0, ïf(x)ï<M = .
7. f (x) , = .
. , .. ,
, ..
= e + ïï
.
.
. f(x) , ¥, +¥ -¥, .
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f (x) = A + a (x),
a () (a () 0 ).
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1) .
2) .
3) , = .
4) , .
, , .
2. f(x) = A + a(x), g(x) = B + b(x),
,
f(x) g(x) = (A + B) + a(x) + b(x)
A + B = const, a() + b() ,
.
3. f(x) = A + a(x), g(x) = B + b(x),
,
A×B = const, a() b() ,
.