.
: .
. , , .
Û
, . . .
, ¹ 0. : , .
.
, . :
) :
;
) n - :
;
) , ,
f(x) = g(x);
) , . .
.
.
.
x2 - 3 = 1;
-3 .
x2 = 4;
-2 2.
, x .
.
x1 = -2 - :
x2 = -2 - .
, -2 2.
. .
, .
. , :
) x - 9 0;
x 9;
) 1 - x 0;
-x -1;
x 1.
: x .
: .
:
.
, , , . .
> 1.
, :
x < -1.
: x >1 x < -1.
: (1)..
. 3 > 9.
3 x > 3 (2). , (1) (2). .(1) (2).
M = (- ; 8) (8; + )- (1).
B = (3; + ) - (2).
|
|
(1)
A = B M =((- ; 8) (8; + ) (3; + ) = (3; 8) (8; + ),
: x (3; 8) (8; + ).
: .
.
: x [-1; 5) (5; + )
0 x = -1, . ( , .. ), :
(-1; 5) 0, 8,
0 8 , , .
: (-5; + ).
:
.
, : x (0; 1) (1; 7) (7; + )
x = 1.
(0;1) 0,5;
(1; 7) 4,
(7; + ) 9,
.
, (0; 1) (1; 7)
: (2x - 6)(3x + 12)(5x + 1)<0.
.
: - 4; - 0,2; 3.
, c "+" "-"....
x (- ; -4) (-0,2; 3).
: 7 - x. . t = , t 0, ( )
t2 = x + 5; x = t2 - 5 t 7 - t2 + 5;
t2 + t - 12 0;
: t R.
t2 + t - 12 = 0;
t1 = -4; t2 = 3.
f(t) = t2 + t - 12; . , , f(x) = (x - 3)(x + 4).
f(4) =4 2 + 4 - 12 = 8 >0;
, f(t) = t2 + t - 12 0, -4 t 3. t 0, 0 t 4. x,
0 3. , 0 x + 5 9, -5 x 4 , ,
x [-5; 3].
: x [-5; 3].
: 2x2 - 8x + 6 > .
.
2 3(x2 - 4x + 3) > .
t = , t > 0 2t2 > t; 2t2 - t > 0; t(2t -1) > 0.
, 1, 0 0,5. :
2t2 > t t > 0,5.
.
> 0,5, x < 1 x > 3.
x2 - 4x + 3 > 0,25;
4x2 - 16x + 11 > 0;
D/4 = 64 - 44 = 20, D > 0.
x1 = , x2 =
, 0,5 < < 1 3 < < 3,5.
x (- ; ) (; + ).
: (- ; ) (; + ).
: 2sin2x - 3sinx - 2 < 0.
.
sinx = t, t [-1; 1] (1),
2t2 - 3t - 2 < 0.
.
|
|
1) Ÿ 2.
2) D = 32 - 4 2(-2) = 9 + 16 = 25, , D > 0.
3) t1 = -0,5; t2 = 2,
t (- ; - 0,5) (2; + ) (2).
(1) (2) [-1; -0,5).
, .
-1 sinx < -0,5. y = sinx.
<="" p="">
x (- + 2 k; - + 2 k), k Z.
: x (- + 2 k; - + 2 k), k Z.
: 3 > lg() + 2.
.
- > 0 x < 0 = |x|, |x| = -x , , x < 0, 3 > lg(-x) + 2. t = , t2 - 3t + 4 < 0.
1) .
2) : t1 = 1, t2 = 2.
3) 1 < t < 2.
1 < < 2. , .
1 < lg(-x) < 4;
-1000 < x < -10.
: (-10000; -10).
.
3 + (20 ) = 35,2,
,
( 3) - = 7 5.
( + 2) - 11( + 2) = 12.
= ,
3 = 96,
+ + + 1 = 0,
5,5n(n 1)(n + 2,5)(n - ) =0.
)2 + =4,
=-5,
= - x. ) =
2 5 = 17.
+ 2 - 15=0;
( - 4) - 7( - 4) +12=0;
+9 - -9=0;
-15 =0;
- 625=0.
1. . . , . - .: , 2013.
2. .., .. , . - .: , 2014.
3. .., .. , . - .: , 2014.
4. .., .. . - .: , 2014.
5. . ., .. . - .: , 194.
6. .. , 10 . - .: , 2013.
7. .. , 11 . - .: , 2013.
8
:
1) : .
2) , .
3) ; , .
:
, .
1. ∆y ∆x , ∆x→0, ..
2 ,, : x , x,..
, , , . : . .
3. : , ..
1 1. , = ² + 2 x = 3. 2. = 3 t 4 + 5 t + 6 (). t = 7. 3. > 0, = | 2 1. y = f (x) = x ² + 6 x +7 = -1. . 2. = 2 t 3 + 3 t 2 + 4 (). t = 2. 3. > 0, = | 3 1. j (t) = t + 6 t ² + 1 2 t (). t = 1. 2. y = f (x) = 3 x 4 + 8 x +9 = -1. . 3. > 0, = |
|
|
1. . . , . - .: , 2013.
2. .., .. , . - .: , 2014.
3. .., .. , . - .: , 2014.
4. .., .. . - .: , 2014.
5. . ., .. . - .: , 194.
6. .. , 10 . - .: , 2013.
7. .. , 11 . - .: , 2013.
9
Mathcad
:
1) : Mathcad.
2) , , .
3) , .