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.
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dx.
2. (8) x .
f(x) x = a ( x-a)
f(x) = f(a) + + + + +
+ + + = .
ex = = 1 + x + |
sin x = = x + + |
cos x = = 1 + + |
1 + x + x2 + x3 + x4 + |
(1 + x)m = 1 + xn = 1 + mx + + |
ln(1+x)= = x , 1 < x ≤ 1 |
arctg x = = x + + , |
. f(x) =2 l. f(x)
, (9)
(10)
. f(x) 1- [ l; l ] [ l; l ] ( ), [ l; l ]. S(x) :
1) f(x) ( l; l);
2) f(x)
x0 , . . S(x0) = 0,5[f(x00)+ f(x0+0)];
3) S(x) = 0,5[f(l 0)+ f( l +0)] = l = l.
f(x) , . . f(x) = f(x), bn = 0,
, (11)
(12)
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x = 2 .
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x = 2 . , , . . . , .
9. , .
z = x2 3, . ( 8), z: . S(z), S(z) = [0, z], , :
= ; S(z) =
z = x23 ,
= .
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2 < x < < x < 2.
10. , x 4.
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11. 0,0001.
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=
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, , : .
0,0001, .
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12. 4 5 () ( ), .
f(x) x = a ( ) f(x) = f(a) + + + + +
+ + = .
= 1, (1) = p, ,
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13.
2p
(. 1).
. (10), l = p, :
(9) :
, . p/2. 2 .
14.
]0; 2[, (. 3).
y ]2; 0[ (. 4), = 4 (. 5), l = 2. , (11), (12),
(10) :
.
]0; 2[ . 6 .
15. ]0; 2[, (. 3).
]2; 0[ (. 7), = 4.
(14) l = 2:
(13) :
.
]0; 2[ . 8 .
1. . . . .: . , 1982. 178 .
2. . . . .: , 1978. 563 .
3. . ., . . . .: , 1980. 467 .
4. . . . . 1. . . . : . , 1985. 220 .
5. . . ( ). . 1. . .: . , 1980. 279 .
6. : . / .: . . , . . . : . , 1992. 36 .
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2. . ...12
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500 .
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