= f () , f (- )= f (x). | = f () Û " Î D (y) Þ f (- )= f (x) |
= f () , f (- )=- f (x). | = f () Û " Î D (y) Þ f (- )=- f (x) = f () Û " Î D (y) Þ f ()=- f (- x) |
, D (y) , : Î D (y), - Î D (y)(. . D (y) - 0 ). | |
= f () , . |
, ________________________. _____________________.
, , .
, ________________________. _____________________.
, , .
() () .
.
.
f (), 1/ f ().
1. :
, f (x) , ( 0; f ( 0)) , 2< x 1<0, ( 2; 1) .
f (x) (- 0; _____) ___________________;
f (x) (- 0; _____) ___________________;
f (x) ______________________________;
, f (x) , ( 0; f ( 0)) , 2> x 1>0, ( 1; 2) .
f (x) (- 0; _____) ___________________;
f (x) (- 0; _____) ___________________;
f (x) ______________________________;
2. , :
3. , , :
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4. :
(+) (-) | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
f (x) , | ||
, | ||
, |
.
= f () , ¹0, , f ( + )= f (x).
. , . , .
5. , f ( x ) T. :
f (2 x) | f (4 x) | |||||
f (0,2 x) | f (0,4 x) | |||||
f (0,5 x) | f (0,25 x) | |||||
f (2+ x) | f (3+ x) | |||||
f (- x) | f (-2 x) | |||||
f (2- x) | f (3- x) | |||||
f (x +4) | f (x +2) | |||||
f (2 x -5) | f (4 x +3) | |||||
f (1,25 x) | f (2,5 x) | |||||
f (4 x)+ f (3 x) | f (2 x)+ f (3 x) | |||||
f (4 x +2)- f (3 x -1) | f (3 x -2)- f (2 x +1) | |||||
f (4 x) f (0,25 x) | f (5 x) f (0,2 x) | |||||
f (0,3 x)/ f (3 x) | f (4 x)/ f (0,4 x) | |||||
f (-1,5 x)+ f (4 x) | f (1,2 x)+ f (-5 x) | |||||
5 f (1-4 x)- f (0,2 x) | 2 f (0,5 x)-5 f (2 x) | |||||
f (4 x) f (- x) | f (- x) f (2-3 x) | |||||
2 f (0,1 x)/ f (3 x) | 3 f (0,4 x)/ f (2 x) | |||||
f (0,5 x)+3 f (0,6 x) | f (0,3 x)+2 f (-0,2 x) | |||||
f (x)-2 f (3 x) | f (4 x)-4 f (x) | |||||
f (4 x) f (0,3 x) | 3 f (0,5 x) f (5 x) |
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6. :
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7. :
8. :
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9. :
:
43-71 ( ) | 40-41 |
. , . . .
( )
Freeth's Nephroid
R : r = R | R : r =2 R cosj | R : r =2 R sinj | |
R : 2 + 2= R 2 : | R : ( - 0)2 + ( - 0)2= R 2 | ||
: ( 2+ 2)2 - 2( 2- 2)2=0, >0 : | : >0 | ||
(a > b) : r = b + a cosj | (a = b) : r = b + a cosj | (a < b) : r = b + a cosj | |
: 2= 3 : | : : | ||
: r = a (1+ cosj), >0 (a = b) | : r = a j, >0 | ||
: , >0 , , . | |||
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