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10. | ||
10. 1. | , , , , . | |
10. 2. | , . : (0, 1), . |
10. 3. | , ? : , - . | |
10. 4. | , y = x 2 x0 . : , f (x 0) = x 02 f (x 0 + D x) = (x 0 + D x)2 D y = (x 0 + D x)2 x 02 = x02 + 2 x 0 × D x + D x 2 x 02 = 2 x 0 × D x + D x 2. 2- , 2- , . | |
10. 5. | , y = sin x x0 . : , f (x 0) = sin x 0 f (x 0+D x) = sin(x 0+D x) D y = sin(x 0 + D x) - sin x 0 = 2sin(D x /2)×cos(x 0 + D x /2). , 2- , : 2- , . |
10. 6. | , 2- 1- . : , D x = x x 0, 1- . | |
10. 7. | , .. x 0 y = f (x) . : : 1- y = sin x , |
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10. |
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10. 1. | 1) , 2) , 3) , 4) ,5) . : 1) = = = = =49-2=47 2) = 3) : x, 100 , , = , 4) = = = . 5) = . | 1), 3), 5) | |
10. 2. | . , . : : . | , | |
10. 3. | : [-1, 1) , . f(x) = | x | 1, .. y = | x | 1 | ||
10. 4. | - , | ||
10. 5. | - ( , ) , ; . | ||
10. 6. | , , . . ; , , ; . | ; . | |
10. 7. | x = 1. x = 1 , . : : , , x = 1 1- . | ||
10. 8. | , = 0 : 1- 0 , , 0 = 0 . , . | ||
10. 9. | . : , . x = 1 2- . | ||
10. 10. | ( ), , , . : , , . 1). 2). 3). . ... | ||
10. 11. | . : [0, 1] (1, 2], = 1 . : : . , = 1 1- . | 1- |
10. 12. | . : , , = 0. , , y = ax, a > 1, - ¥. , y = 1/ x , 0 < 0. , , , y = ax, a > 1, +¥. , , 0 > 0. , , = 0 2- . | = 0 2- . |
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10. 13. | , = 0 : . . , = 1 , : | |
10. 14. | sinx x + 1 = 0? : f(x) = sinx x + 1, , y = sinx y = -x + 1. , , f(0) = 1, f(2p) = -2p + 1 < 0. , [0, 2p], . | |
10. 15. | . : , . , , . | |
10. 16. | [-2, 2]? : [-2, 2]. , f (-2)=1, f (2) = 5. c Î (-2, 2) , |
10. 17. | , . : , , . , , . , , . : , . . , , . . . |