4 - циклические вычислительные процессы общее
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13. Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
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ɰɢɤɥɚ P =∏ln (n +2x).
n=1
14. Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
S = ∑4 |
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n=1 (n + x) |
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15. Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
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ɰɢɤɥɚ P =∏ x + |
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n=1 |
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16. Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
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n=1 (n + |
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17. Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
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18. Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
S = ∑k 2n .
n=1 n2
19.Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
k 3n+1
S =∑n=1 n3 .
20. Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ |
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ɰɢɤɥɚ P =∏ |
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21.Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
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ɰɢɤɥɚ P =∏(2x −n2 ). |
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n=1 |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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S =∑k |
sin (π n / 9). |
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n=1 |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ |
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ɰɢɤɥɚ P =∏(1+ |
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sin (n π / k ) |
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n=1 |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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S =∑k |
n cos(π n /8). |
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n=1 |
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25. |
Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ |
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1+ n |
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ɰɢɤɥɚ P =∏ |
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n=1 |
x2 + n2 |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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S = ∑k |
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n=1 |
x2 + n2 |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ |
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ɰɢɤɥɚ P =∏ |
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n=1 |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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S = ∑k |
1 + n3 . |
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29. |
n=1 |
1 +n2 |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ |
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Ɍɪɢɠɞɵ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɫɭɦɦɵ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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S = ∑k |
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n=1 n |
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Список задач №2 для лабораторной работы «Циклические вычислительные процессы»
1. |
Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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f (x)= |
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(x / a +a) ɧɚ ɢɧɬɟɪɜɚɥɟ x [−2; 2.5], |
x = 0,35 , ɭɤɚɡɚɜ |
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ɡɧɚɱɟɧɢɹ ɚɪɝɭɦɟɧɬɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɮɭɧɤɰɢɸ ɧɟɥɶɡɹ ɜɵɱɢɫɥɢɬɶ. |
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2. |
Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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2x + a |
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f (x)= |
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ɧɚ ɢɧɬɟɪɜɚɥɟ x [−4; 5], x =1, ɭɤɚɡɚɜ ɡɧɚɱɟɧɢɹ |
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x3 −2x2 − x +2 |
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ɚɪɝɭɦɟɧɬɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɮɭɧɤɰɢɸ ɧɟɥɶɡɹ ɜɵɱɢɫɥɢɬɶ. |
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3. |
Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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f (x)= |
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x3 −6x2 +11x −6 ɧɚ ɢɧɬɟɪɜɚɥɟ x [0; 3.5], x = 0, 4 , ɭɤɚɡɚɜ |
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ɡɧɚɱɟɧɢɹ ɚɪɝɭɦɟɧɬɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɮɭɧɤɰɢɸ ɧɟɥɶɡɹ ɜɵɱɢɫɥɢɬɶ. |
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4. |
Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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f (k )= |
sin (k π / N ) |
ɧɚ ɢɧɬɟɪɜɚɥɟ k [−6; 3], |
k =1, ɭɱɬɹ ɩɪɢ ɷɬɨɦ, ɱɬɨ |
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sin (0) |
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k π / N |
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Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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f (x)= A |
sin (x3 −2x2 − x + 2) |
ɧɚ ɢɧɬɟɪɜɚɥɟ x [−2; 3], |
x = 0,5 , ɭɱɬɹ |
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x3 −2x2 |
− x + 2 |
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ɩɪɢ ɷɬɨɦ, ɱɬɨ |
sin (0) |
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6. |
0 |
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Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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f (x)= 3 2x +2 2−x ɧɚ ɢɧɬɟɪɜɚɥɟ x [−2; 5], x = 0,75 , ɭɤɚɡɚɜ x +5x + 2x −8
ɡɧɚɱɟɧɢɹ ɚɪɝɭɦɟɧɬɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɮɭɧɤɰɢɸ ɧɟɥɶɡɹ ɜɵɱɢɫɥɢɬɶ.
7. Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɰɟɥɭɸ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
ɰɢɤɥɚ |
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+1, |
при k четном |
ɧɚ ɢɧɬɟɪɜɚɥɟ k [−2; 5], k =1. |
f (k )= k |
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k −a, |
при k нечетном |
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8. Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɰɟɥɭɸ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
ɰɢɤɥɚ |
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+ a, при k четном |
ɧɚ ɢɧɬɟɪɜɚɥɟ k [−3; 8], k =1. |
f (k )= k |
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a k, при k нечетном |
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9. Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f (x)= |
e−ax +eax |
ɧɚ ɢɧɬɟɪɜɚɥɟ x [−3; 6], x =1, ɭɤɚɡɚɜ ɡɧɚɱɟɧɢɹ |
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x3 −7x −6 |
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ɚɪɝɭɦɟɧɬɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɮɭɧɤɰɢɸ ɧɟɥɶɡɹ ɜɵɱɢɫɥɢɬɶ.
10.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f (x)= |
ax2 +3 |
ɧɚ ɢɧɬɟɪɜɚɥɟ x [−9; 21], x =3, ɭɤɚɡɚɜ ɡɧɚɱɟɧɢɹ |
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sin (πx / 6) |
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ɚɪɝɭɦɟɧɬɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɮɭɧɤɰɢɸ ɧɟɥɶɡɹ ɜɵɱɢɫɥɢɬɶ.
11. Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
(x + a)2 , если |
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sin (x) |
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ɧɚ ɢɧɬɟɪɜɚɥɟ x [−3; 2], x = 0,3 . |
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f (x)= |
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sin (x) |
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x +1, |
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12.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
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a, если |
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cos(x) |
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x + |
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f (x)= |
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cos(x) |
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ɧɚ ɢɧɬɟɪɜɚɥɟ x [−2; 7], x = 0, 4 .
13.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
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еслиx |
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+5x |
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+ 2x −8 |
≠ 0 |
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f (x)= |
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ɧɚ ɢɧɬɟɪɜɚɥɟ |
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x3 +5x2 + 2x −8 |
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еслиx |
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+ 2x −8 |
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a x, |
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x [−2; 7], |
x = 0,75 . |
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13
14.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
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еслиx |
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+9x |
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+26x + 24 |
≠ 0 |
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f (x)= |
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ɧɚ |
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x3 +9x2 + 26x +24 |
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ɢɧɬɟɪɜɚɥɟ x [0; 7], x = 0,5 . |
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15. Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
2x +a |
ɧɚ ɢɧɬɟɪɜɚɥɟ x [−4; 5], |
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f (x)= x3 −2x2 − x +2 |
x =1, ɭɤɚɡɚɜ ɡɧɚɱɟɧɢɹ |
ɚɪɝɭɦɟɧɬɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɮɭɧɤɰɢɸ ɧɟɥɶɡɹ ɜɵɱɢɫɥɢɬɶ.
16.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f (x)=sin (a tg (x)) ɧɚ ɢɧɬɟɪɜɚɥɟ x [−4; 5], |
x = 0, 43, ɭɤɚɡɚɜ ɩɪɢ |
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ɷɬɨɦ ɩɪɟɜɵɲɚɟɬ ɦɨɞɭɥɶ ɜɵɱɢɫɥɟɧɧɨɣ ɮɭɧɤɰɢɢ |
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17.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ f (x)=sin2 (ctg (x + a)) ɧɚ ɢɧɬɟɪɜɚɥɟ x [−2; 8], x = 0,6 , ɭɤɚɡɚɜ ɩɪɢ
ɷɬɨɦ ɩɪɟɜɵɲɚɟɬ ɦɨɞɭɥɶ ɜɵɱɢɫɥɟɧɧɨɣ ɮɭɧɤɰɢɢ 12 , ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ. 18.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ f (x)= tg(x2 +3 k x) ɧɚ ɢɧɬɟɪɜɚɥɟ x [−1; 7], x = 0,6 , ɭɤɚɡɚɜ ɩɪɢ
ɷɬɨɦ ɞɟɥɢɬɫɹ ɢɥɢ ɧɟ ɞɟɥɢɬɫɹ ɧɚ 3 ɰɟɥɚɹ ɱɚɫɬɶ ɜɵɱɢɫɥɟɧɧɨɣ ɮɭɧɤɰɢɢ. 19.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f (x)= 2a x + x2 +ax −3 ɧɚ ɢɧɬɟɪɜɚɥɟ x [−3; 8], x = 0,8 , ɭɤɚɡɚɜ ɩɪɢ
ɷɬɨɦ ɞɟɥɢɬɫɹ ɢɥɢ ɧɟ ɞɟɥɢɬɫɹ ɧɚ 5 ɰɟɥɚɹ ɱɚɫɬɶ ɜɵɱɢɫɥɟɧɧɨɣ ɮɭɧɤɰɢɢ. 20.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f (x)=ctg(x3 −k x) ɧɚ ɢɧɬɟɪɜɚɥɟ x [−3; 5], x = 0,6 , ɭɤɚɡɚɜ ɩɪɢ ɷɬɨɦ
ɩɪɟɜɵɲɚɟɬ ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɟ 12 ɦɨɞɭɥɶ ɞɪɨɛɧɨɣ ɱɚɫɬɢ
ɜɵɱɢɫɥɟɧɧɨɣ ɮɭɧɤɰɢɢ.
21.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f (x)= |
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3a x sin (x) |
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ɧɚ ɢɧɬɟɪɜɚɥɟ x [−3.5; 6], |
x = 0,7 , ɭɤɚɡɚɜ ɩɪɢ |
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ɷɬɨɦ ɩɪɟɜɵɲɚɟɬ ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɟ 13 |
ɦɨɞɭɥɶ ɞɪɨɛɧɨɣ ɱɚɫɬɢ |
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ɜɵɱɢɫɥɟɧɧɨɣ ɮɭɧɤɰɢɢ. |
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22.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f |
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= |
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−sin |
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)) |
ɧɚ ɢɧɬɟɪɜɚɥɟ x |
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ɷɬɨɦ ɩɪɟɜɵɲɚɟɬ ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɟ |
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ɦɨɞɭɥɶ ɞɪɨɛɧɨɣ ɱɚɫɬɢ |
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ɜɵɱɢɫɥɟɧɧɨɣ ɮɭɧɤɰɢɢ.
23.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ f (x)= 3kx +2kx ɧɚ ɢɧɬɟɪɜɚɥɟ x [−2.5; 7], x = 0,6 , ɭɤɚɡɚɜ ɩɪɢ ɷɬɨɦ
ɩɪɟɜɵɲɚɟɬ ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɨɫɬɚɬɨɤ ɨɬ ɞɟɥɟɧɢɹ ɰɟɥɨɣ ɱɚɫɬɢ ɮɭɧɤɰɢɢ ɧɚ 3 ɨɫɬɚɬɨɤ ɨɬ ɞɟɥɟɧɢɹ ɰɟɥɨɣ ɱɚɫɬɢ ɷɬɨɣ ɮɭɧɤɰɢɢ ɧɚ 4.
14
24.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ f (x)= 3x (cos(x2 )+sin (x)) ɧɚ ɢɧɬɟɪɜɚɥɟ x [−3.5; 6], x = 0,7 ,
ɭɤɚɡɚɜ ɩɪɢ ɷɬɨɦ ɩɪɟɜɵɲɚɟɬ ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɮɭɧɤɰɢɹ ɡɧɚɱɟɧɢɹ k sin (x) .
25.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ f (x)= 3−k2 x + 2−kx2 ɧɚ ɢɧɬɟɪɜɚɥɟ x [−1.5; 6], x = 0, 4 , ɭɤɚɡɚɜ ɩɪɢ ɷɬɨɦ ɩɪɟɜɵɲɚɟɬ ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɮɭɧɤɰɢɹ ɡɧɚɱɟɧɢɹ 1k cos(x) .
26.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
f (x)= 2kx |
( |
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, ɭɤɚɡɚɜ ɩɪɢ |
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x2 + x −1 ɧɚ ɢɧɬɟɪɜɚɥɟ x [−1.5; 5], x = 0, 4 |
ɷɬɨɦ ɩɪɟɜɵɲɚɟɬ ɢɥɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɨɫɬɚɬɨɤ ɨɬ ɞɟɥɟɧɢɹ ɰɟɥɨɣ ɱɚɫɬɢ ɮɭɧɤɰɢɢ ɧɚ 2 ɨɫɬɚɬɨɤ ɨɬ ɞɟɥɟɧɢɹ ɰɟɥɨɣ ɱɚɫɬɢ ɷɬɨɣ ɮɭɧɤɰɢɢ ɧɚ 3.
27.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ
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x = 0,35 .
28.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ ɰɢɤɥɚ |
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f (x)= A |
sin (x3 + x2 −4x −4) |
ɧɚ ɢɧɬɟɪɜɚɥɟ x [−3; 3], |
x = 0,5 , ɭɱɬɹ |
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ɩɪɢ ɷɬɨɦ, ɱɬɨ sin0(0) =1.
29.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɰɟɥɭɸ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
ɰɢɤɥɚ |
a +12div k, при k четном |
ɧɚ ɢɧɬɟɪɜɚɥɟ k [−10; 10], |
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k2 , |
при k нечетном |
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k =1.
30.Ɍɪɢɠɞɵ ɩɪɨɬɚɛɭɥɢɪɨɜɚɬɶ ɰɟɥɭɸ ɮɭɧɤɰɢɸ, ɢɫɩɨɥɶɡɭɹ ɬɪɢ ɪɚɡɥɢɱɧɵɯ
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ɧɚ ɢɧɬɟɪɜɚɥɟ k [−4; 8], |
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15
Список задач №3 для лабораторной работы «Циклические вычислительные процессы»
ɜɥɨɠɟɧɧɵɟ ɰɢɤɥɵ ɫ ɮɢɝɭɪɧɵɦ ɜɵɜɨɞɨɦ
1. |
ȼɜɟɫɬɢ ɰɟɥɵɟ k ɢ n , ɟɫɥɢ k < n , ɬɨ ɜɵɜɟɫɬɢ ɬɚɛɥɢɰɭ ɭɦɧɨɠɟɧɢɹ ɞɥɹ |
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ɱɢɫɟɥ ɨɬ k ɞɨ n . ɇɚɩɪɢɦɟɪ, ɞɥɹ k = 2 ɢ n = 4: |
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2* |
3* |
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2* |
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4* |
8 |
12 |
16 |
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ȼɜɟɫɬɢ ɰɟɥɨɟ n , ɟɫɥɢ n >0 , ɜɵɜɟɫɬɢ ɡɧɚɱɟɧɢɹ F – ɮɚɤɬɨɪɢɚɥɨɜ ɨɬ 1 ɞɨ |
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n ɜ ɤɚɠɞɨɣ ɫɬɪɨɤɟ ɜ ɤɨɥɢɱɟɫɬɜɟ ɪɚɡ ɪɚɜɧɨɦ ɨɫɬɚɬɤɭ ɨɬ ɞɟɥɟɧɢɹ F +1 ɧɚ |
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10 (ɧɨɦɟɪ ɫɬɪɨɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɚɪɝɭɦɟɧɬɭ ɮɚɤɬɨɪɢɚɥɚ). ɇɚɩɪɢɦɟɪ, ɞɥɹ n =6 :
11
22 2
6 6 6 6 6 6 6
24 24 24 24 24
120
720
3. ȼɜɟɫɬɢ ɞɜɚ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɥɚ N ɢ M . ȿɫɥɢ M > N , ɬɨ ɜɵɜɟɫɬɢ
M − N ɫɬɪɨɤ, ɜ ɤɚɠɞɨɣ ɫɬɪɨɤɟ ɜɵɜɨɞɹɬɫɹ ɱɢɫɥɚ ɨɬ N ɞɨ M ɱɢɫɥɨ ɪɚɡ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɜɵɜɨɞɢɦɨɦɭ ɱɢɫɥɭ. ɇɚɩɪɢɦɟɪ, ɞɥɹ N =3 ɢ M =6 : 3 3 3 4 4 4 4
5 5 5 5 5
6 6 6 6 6 6
4. ȼɜɟɫɬɢ ɧɚɬɭɪɚɥɶɧɨɟ ɱɢɫɥɨ
4.
16
N
34
43
7.ȼɜɟɫɬɢ ɰɟɥɨɟ n , ɟɫɥɢ n >3 , ɬɨ ɜɵɜɟɫɬɢ ɜɫɟ ɬɪɨɣɤɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɱɢɫɟɥ, ɤɨɬɨɪɵɟ ɜ ɫɭɦɦɟ ɞɚɸɬ n . ɇɚɩɪɢɦɟɪ, ɞɥɹ n =6 :
1+1+4, 1+2+3, 1+3+2, 1+4+1 2+1+3, 2+2+2, 2+3+1 3+1+2, 3+2+1 4+1+1
8.ȼɜɟɫɬɢ ɰɟɥɵɟ k ɢ n , ɟɫɥɢ k < n , ɬɨ ɜɵɜɟɫɬɢ ɬɚɛɥɢɰɭ ɫɥɨɠɟɧɢɹ ɞɥɹ ɱɢɫɟɥ ɨɬ k ɞɨ n . ɇɚɩɪɢɦɟɪ, ɞɥɹ k =3 , n =6 :
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3+ |
4+ |
5+ |
6+ |
3+ |
6 |
7 |
8 |
9 |
4+ |
7 |
8 |
9 |
10 |
5+ |
8 |
9 |
10 |
11 |
6+ |
9 |
10 |
11 |
12 |
9.ȼɜɟɫɬɢ ɰɟɥɨɟ n , ɟɫɥɢ n >0 , ɜɵɜɟɫɬɢ ɱɢɫɥɚ «ɬɪɟɭɝɨɥɶɧɢɤɨɦ», ɫɨɫɬɨɹɳɢɦ ɢɡ n ɫɬɪɨɤ. ɇɚɩɪɢɦɟɪ, ɞɥɹ n =5 :
****1****
***121***
**12321**
*1234321*
123454321
10.
17
+>>>>>>>>+
+<<<<<<<<+
++++++++++
13.ȼɜɟɫɬɢ ɰɟɥɨɟ N , ɟɫɥɢ N >0 , ɬɨ ɫɨɫɬɚɜɢɬɶ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜɵɜɨɞɢɬ ɱɢɫɥɨ «*» ɜ ɤɨɥɢɱɟɫɬɜɟ ɨɬ N ɞɨ 1 ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɜ ɤɚɠɞɨɣ ɫɬɪɨɤɟ ɧɚ ɟɞɢɧɢɰɭ ɢ ɩɟɪɟɤɪɟɫɬɧɵɦ ɨɬɫɬɭɩɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ N =5 :
*****
****
***
**
*
14.ȼɜɟɫɬɢ 2 ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɥɚ N ɢ M . ȼɵɜɟɫɬɢ ɩɪɹɦɨɭɝɨɥɶɧɢɤ M ×N , ɫɮɨɪɦɢɪɨɜɚɧɧɵɣ ɡɧɚɤɨɦ «+», ɜɧɭɬɪɢ ɡɚɩɨɥɧɟɧɧɵɣ ɡɧɚɤɚɦɢ «>» ɢ «<» ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɱɢɫɥɚ ɡɧɚɤɨɜ «>» ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɭɜɟɥɢɱɟɧɢɟɦ «<». ɇɚɩɪɢɦɟɪ, ɞɥɹ N =6 ɢ M =7 ɜɵɜɨɞ ɬɚɤɨɜ:
+++++++
+>>>>>+
+>>>><+
+>>><<+
+>><<<+
+++++++
15.ɇɚɣɬɢ ɜɫɟ ɬɪɨɣɤɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ( x, y, z ), ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ ɭɫɥɨɜɢɸ 10 x +20 y +30 z = N . ɇɚɬɭɪɚɥɶɧɨɟ N ɜɜɨɞɢɬɫɹ ɫ
ɤɥɚɜɢɚɬɭɪɵ. ȿɫɥɢ ɪɟɲɟɧɢɣ ɧɟɬ, ɬɨ ɜɵɞɚɬɶ ɫɨɨɛɳɟɧɢɟ ɨɛ ɷɬɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ N =90:
1, 1, 2 2, 2, 1 4, 1, 1
16.ȼɜɟɫɬɢ ɰɟɥɨɟ n , ɟɫɥɢ n >0 , ɬɨ ɜɵɜɟɫɬɢ ɱɢɫɥɨ en ɜ ɤɚɠɞɨɣ ɫɬɪɨɤɟ ɱɢɫɥɚ ɨɬ 1 ɞɨ n , ɫɥɟɜɚ ɨɬ ɱɢɫɥɚ ɜɵɜɟɫɬɢ ɡɧɚɤ “#” ɫɬɨɥɶɤɨ ɪɚɡ, ɱɟɦɭ ɪɚɜɟɧ ɨɫɬɚɬɨɤ ɨɬ ɞɟɥɟɧɢɹ ɰɟɥɨɣ ɱɚɫɬɢ ɱɢɫɥɚ ɧɚ 10. ɇɚɩɪɢɦɟɪ, ɞɥɹ n =5 :
## 2,718
####### 7,389 20,085
#### 54,598
######## 148,413
17.ɇɚɣɬɢ ɜɫɟ ɬɪɨɣɤɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ( x, y, z ), ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ ɭɫɥɨɜɢɸ x y +5 z = N . ɇɚɬɭɪɚɥɶɧɨɟ N ɜɜɨɞɢɬɫɹ ɫ ɤɥɚɜɢɚɬɭɪɵ. ȿɫɥɢ
ɪɟɲɟɧɢɣ ɧɟɬ, ɬɨ ɜɵɞɚɬɶ ɫɨɨɛɳɟɧɢɟ ɨɛ ɷɬɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ N =12 : 1, 7, 1 1, 2, 2 2, 1, 2 7, 1, 1
18
18.Ⱦɥɹ ɨɤɪɭɠɧɨɫɬɢ ɪɚɞɢɭɫɚ
19
21 – 1, 3, 7, 21
22 – 1, 2, 11, 22
24.ɇɚɣɬɢ ɜɫɟ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ ɧɚ ɧɚɬɭɪɚɥɶɧɨɦ ɩɪɨɦɟɠɭɬɤɟ [a,b],
ɤɨɬɨɪɵɟ ɞɟɥɹɬɫɹ ɧɚ 3. Ʉɚɠɞɨɟ ɱɢɫɥɨ ɜɵɜɨɞɢɬɶ ɜ ɨɬɞɟɥɶɧɨɣ ɫɬɪɨɤɟ ɫɬɨɥɶɤɨ ɪɚɡ, ɫɤɨɥɶɤɨ ɩɨɥɭɱɚɟɬɫɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɟɝɨ ɞɟɥɟɧɢɹ ɧɚ 3. ɇɚɩɪɢɦɟɪ, ɞɥɹ a =10 , b =19:
12 12 12 12
15 15 15 15 15
18 18 18 18 18 18
25.ɇɚɣɬɢ ɜɫɟ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ ɧɚ ɧɚɬɭɪɚɥɶɧɨɦ ɩɪɨɦɟɠɭɬɤɟ [a,b],
ɤɨɬɨɪɵɟ ɞɟɥɹɬɫɹ ɧɚ 3. Ʉɚɠɞɨɟ ɱɢɫɥɨ ɜɵɜɨɞɢɬɶ ɜ ɨɬɞɟɥɶɧɨɣ ɫɬɪɨɤɟ, ɫɩɪɚɜɚ ɡɚɩɢɫɚɬɶ ɫɤɨɥɶɤɨ ɪɚɡ ɟɝɨ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ 3. ɇɚɩɪɢɦɟɪ, ɞɥɹ a =13 , b = 29 :
15 – 1
18 – 2
21 – 1
24 – 2
27 – 3
26.ɇɚɩɢɫɚɬɶ ɩɪɨɝɪɚɦɦɭ ɞɥɹ ɜɨɡɜɟɞɟɧɢɹ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɬ 1 ɞɨ N , ɜɜɟɞɺɧɧɨɝɨ ɫ ɤɥɚɜɢɚɬɭɪɵ, ɜ ɬɪɟɬɶɸ ɫɬɟɩɟɧɶ ɛɟɡ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɨɩɟɪɚɰɢɢ ɭɦɧɨɠɟɧɢɹ, ɭɱɢɬɵɜɚɹ ɫɥɟɞɭɸɳɭɸ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ: 13 =1,
23 =3 +5, 33 =7 +9 +11, 43 =13 +15 +17 +19 ɢ ɬ.ɞ. ɉɪɢ ɜɵɜɨɞɟ ɱɢɫɥɚ ɩɨɤɚɡɵɜɚɬɶ ɫɥɚɝɚɟɦɵɟ ɟɝɨ ɫɨɫɬɚɜɥɹɸɳɢɟ. ɇɚɩɪɢɦɟɪ, ɞɥɹ N = 4 :
1 = 1
8 = 3+5
27 = 7+9+11
64 = 13+15+17+19
27.ɉɭɫɬɶ ɜ ɧɟɤɨɬɨɪɨɣ ɫɬɪɚɧɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɭɩɸɪɵ ɞɨɫɬɨɢɧɫɬɜɨɦ 1,2,5,10. ɇɚɣɬɢ ɞɥɹ ɜɜɟɞɺɧɧɨɝɨ ɰɟɥɨɝɨ N ɦɢɧɢɦɚɥɶɧɵɣ ɧɚɛɨɪ ɤɭɩɸɪ, ɢɡ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɫɭɦɦɭ N ɫ ɭɤɚɡɚɧɢɟɦ ɫɤɨɥɶɤɨ ɢ ɤɚɤɢɯ ɤɭɩɸɪ ɩɨɬɪɟɛɭɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ ɧɚɛɨɪɚ ɧɭɠɧɨɣ ɫɭɦɦɵ. ɇɚɩɪɢɦɟɪ, ɞɥɹ
N = 27 : 10 – 2 5 – 1 2 – 1 1 – 0
28.ȼɜɟɫɬɢ ɰɟɥɨɟ n , ɟɫɥɢ n >0 , ɬɨ ɜɵɜɟɫɬɢ ɜ ɤɚɠɞɨɣ ɫɬɪɨɤɟ ɡɧɚɱɟɧɢɹ ɜɫɟɯ ɮɚɤɬɨɪɢɚɥɨɜ ɨɬ 1 ɞɨ n ɫ ɭɤɚɡɚɧɢɟɦ ɩɪɢ ɷɬɨɦ ɫɨɦɧɨɠɢɬɟɥɟɣ ɢɡ ɤɨɬɨɪɵɯ
ɨɧ ɫɨɫɬɨɢɬ. ɇɚɩɪɢɦɟɪ, ɞɥɹ n 5 ɮɨɪɦɚɬ ɜɵɜɨɞɚ ɬɚɤɨɜ: 1=1 1*2=2 1*2*3=6
1*2*3*4=24
1*2*3*4*5=120
20