f (x)=0. | (1) |
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f (x) = sin8 x - 0,5 ( .3), , , , [1,2], , .
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. 3. f (x)=sin8 x -0,5, [1,2]
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1. f (x) [a,b], (), (1).
f (x) (.[5], 16, c.31). :
2. f (x) [a,b], [a,b], f (x)>0 (f (x)<0) [a,b], [a,b] (1).
f (x) =x-ex-2, .4. [0,1], [0,1],
f (0) = - e -2= -0,13534<0, f (1)=1- e -1= 0,632121>0. : f (x)=1 - ex-2. x Î[0,1] . , f (x) =x-ex-2 [0,1] .
. 4. f (x) =x-ex-2, [0,1],
, f (x) ( ), f (x) . , :
3. f (x) [a,b], [a,b],
f (x)>0 (f (x)<0) [a,b], [a,b] (1).
, , "" h ( h ) f (x), .. f (x)× f (x+h) < 0.
, (1) f (x). , (1) , f (x), , . (1)
f 1(x)= f 2(x) | (2) |
, y = f 1(x) y = f 2(x) , f (x). (2) y = f 1(x), y = f 2(x).
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3 x -2 x -4=0
1) ;
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3) MS Excel.
2.
f (x)=3 x -2 x -4. , , .. x Î(-¥,¥). , . ( ) , f (x)= 3 x ln3-2. : 3 x ln3-2=0; 3 x = ; lg3 x =lg ; x lg3=lg2-lg(ln3); x = .
, (-¥,1) (f (x)<0 x Î(-¥,1)) (1, +¥) (f (x)>0 x Î(1, +¥)).
f (x) (Sgn f (x)), x :
a) ( ) ;
b) ( ):
x | -¥ | +¥ | |
Sgn f (x) | + | - | + |
f (-100)=3-100-2(-100)-4>0; f (1)=31-2×1-4<0; f (100)= 3100-2×100-4>0.
, . , , , 1. f (x):
x | -2 | -1 | |||
Sgn f (x) | + | - | - | - | + |
f (-2)= 3-2-2×(-2)-4=0,111111>0; f (-1)=3-1-2(-1)-4=-1,66667<0;
f (0)=30-2×0-4=-3<0; f (2)= 32-2×2-4=1>0.
, , : x 1Î[-2,-1], x 2Î[1,2].
3. .
f (x)=3 x -2 x -4 MS Excel, . :
3 x -2 x -4=0 3 x =2 x +4 y =3 x, y =2 x +4:
, y = f (x) y = f (x) , , y 1 y 2 .
, : x 1Î[-2,-1], x 2Î[1,2].
4. MS Excel. - .
f (x)=3 x -2 x -4 f (x)= 3 x ln3-2 , . , . , , 0,5. .2 3 (. ) , 3 x -2 x -4=0 [-2,-1] [1,2]. x -2,5 2,5 0,5. , . , x, f (x) f (x) A1, B1 1 . , , .
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. 5. f (x)=3 x -2 x -4
f (x)=3 x -2 x -4.
.5 , f (-2) = 0,11111>0, f (-1)=-1,666<0 f (x)<0 x [-2,-1]. 2 (. . 6), , [-2,-1] .
[1,2], , .
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1
1
. | . | ||
3 x -1-4- x =0; | 2lg x - +1=0; | ||
2 x -lg x -7=0; | e x + x +1=0; | ||
2e x =5 x -2; | Sin(x +1)=0,5 x; | ||
x 4- x -1=0; | x 3-6 x =8; | ||
5sin x = x -1; | 3 x +2 x -3=0; | ||
2arctg x -3 x +2=0; | arctg(x -1)+2 x =0; | ||
2 x 4- x 2-10=0; | 3 x -2 x +5=0; | ||
2 x -3 x -2=0; | 3 x 4+4 x 3-12 x 2-5=0; | ||
x 22 x =3; | arctg x - =0; | ||
x 3-3 x 2+9 x -8=0; | x lg x -1,2=0. |
2.