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Первообразная (ЕГЭ-№12)
1.
ДР-0Кл/P 13.12.23г
2.
3.
F x f x'
1 3x 2
F x
2 x C
5 2
1 3 42
F 4
2 4 C 5
5 2
1
24 8 C 5
5
32 5C 25
1
f x 3 x 2
5
5C 7;
C 1,4
2
1 3x
F x
2 x 1,4
5 2
1 3
F 1 2 1,4
5 2
0,7
4.
F x f x'
F x x 2 x 3; F 3 9
'
2
F‘(x)
+
F(x)
-1
max
−
0
33
F 3 32 3 3 C 9;
3
C 0
x3
F x x 2 3x
3
3
min
x3
F x x 2 3x C
3
+
6
x
F 0 0;
63
2
F 6 6 3 6
3
F 6 72 36 18
18
5.
F x f x'
f x 3 2 x
1
F x 3x 2 C
x
1
F x 3x 2
x
3 1 C 2
1
F 1,5 4
2
C 0
2,5
3
6.
F x f xf x 6 x
x 1
F x 6
C
1
6
F x
x
'
6
F x C
x
6
F 2
C 3
2
3 C 3
C 0
6
6
2
x
x
x 0
2
x2 x
x 0
1
7.
F x f x'
22
f x
2
2 x
F x 2 x 22 x C
F x 2 x 22 x 67
F 4 8 22 4 C 15
F 9 18 22 3 67
52 C 15
C 67
17
8.
F x f x2
f x x
3
'
F 1 2 1 3;
2
2 3 2
F x x : C
3
3
2
3
F x x C
F 1 1 C 1
C 2
F 1 1
1
3
2
3
F x x 2
2
3
F 8 8 2
2
F 8 2
2
3 3
F 8 4 2
2
9.
F 0F ' x f x
F x 3 cos x 2 sin x C
F 3 cos 2 sin C 0;
3 C 0;
C 3
F x 3 cos x 2 sin x 3
F 0 3 cos 0 2 sin 0 3
F 0 3 3
6
10.
F x f x'
cos 4 x
F x 2 x
C;
4
cos
F
C 3 ;
4
4 2
1
C 3 ;
2 4
7 1
C
;
2 4
cos 4 x 7 1
F x 2 x
4
2 4
7 14 cos 7 7 1
F
4
4
2 4
4
7 7 1 7 1
F
4 2 4 2 4
0
11.
F ' x f xF x e 2 x 3x C
F x e x 2 x 2 3x 5
F 1 e 2 3 C e
F 0 e 0 2 0 3 0 5
x
C 5
2
F 0 1 5
4
12.
F ' x f x 0 для x 0; 2 F x на 0; 2F 2 e
2
F x e x x 2 x C
F 2 e 2 2 2 2 C e 2
C 6
min F x F 0
0; 2
F 0 e 0 0 2 0 6
F 0 1 6
5
13.
F ' x f x 0 для x 2; F x на 2;xmin 22
22
14.
F ' x x 5 ln x 1D f : x 1
+
+
F‘(x)
F(x)
2
max
1
4
3
−
5
min
14
3
x
xmax 2
4 14
3; 3
2
15.
ТР-1Д/З на 15.12.23г