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Ɇɢɧɢɫɬɟɪɫɬɜɨ ɨɛɪɚɡɨɜɚɧɢɹ Ɋɟɫɩɭɛɥɢɤɢ Ȼɟɥɚɪɭɫɶ ȻȿɅɈɊɍɋɋɄɂɃ ɇȺɐɂɈɇȺɅɖɇɕɃ ɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼȿɊɋɂɌȿɌ
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Ʉɚɮɟɞɪɚ «ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ ʋ 1» |
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Ɇɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ Ȼ |
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ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ ʋ 2 |
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ɩɨ ɦɚɬɟɦɚɬɢɤɟɣ |
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ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɢɧɠɟɧɟɪɧɨ-ɬɟɯɧɢɱɟɫɤɢɯɢ |
ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ |
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ɡɚɨɱɧɨɣ ɮɨɪɦɵ ɨɛɭɱɟɧɢɹ |
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ɗɥɟɤɬɪɨɧɧɨɟ ɭɱɟɛɧɨɟ ɢɡɞɚɧɢɟ |
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Ɇɢɧɫɤ 2 0 1 1
ɍȾɄ 512.64(075.8) |
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ɋɨɫɬɚɜɢɬɟɥɢ: |
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Ⱥ.ɇ. Ⱥɧɞɪɢɹɧɱɢɤ, Ⱥ.ȼ. Ɇɟɬɟɥɶɫɤɢɣ, ɇ.Ⱥ. Ɇɢɤɭɥɢɤ, |
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Ƚ.Ⱥ. Ɋɨɦɚɧɸɤ, ȼ.ɂ. ɘɪɢɧɨɤ |
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Ɋɟɰɟɧɡɟɧɬɵ: |
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Ʌ.ɂ. Ɇɚɣɫɟɧɹ, ɡɚɜ. ɤɚɮɟɞɪɨɣ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɞɢɫɰɢɩɥɢɧ ɂɂɌ |
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ȻȽɍɂɊ; |
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Ⱥ.ɇ. Ɋɭɞɵɣ, ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ «ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ ʋ 2» ȻɇɌɍ, ɤɚɧɞɢɞɚɬ |
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ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɧɚɭɤ |
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ɫɬɭɞɟɧɬɨɜ |
ɩɟɪɜɨɝɨ ɤɭɪɫɚ |
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ɇɚɫɬɨɹɳɚɹ ɪɚɡɪɚɛɨɬɤɚ ɩɪɟɞɧɚɡɧɚɱɟɧɚ ɞɥɹ |
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ɡɚɨɱɧɨɝɨ ɨɬɞɟɥɟɧɢɹ ɢɧɠɟɧɟɪɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ. |
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ɫɜɟɞɟɧɢɹ ɢɡ |
ɩɪɨɝɪɚɦɦɧɨɝɨ |
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Ɋɚɛɨɬɚ ɫɨɞɟɪɠɢɬ ɨɫɧɨɜɧɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ |
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ɦɚɬɟɪɢɚɥɚ, ɩɨɞɪɨɛɧɵɟ ɪɟɲɟɧɢɹ ɬɢɩɨɜɵɯ ɩɪɢɦɟɪɨɜ, ɜɨɩɪɨɫɵ ɞɥɹ ɫɚɦɨɤɨɧɬɪɨɥɹ, ɚ |
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ɬɚɤɠɟ ɤɨɧɬɪɨɥɶɧɵɟ ɡɚɞɚɧɢɹ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɬɟɦɚɦ ɤɭɪɫɚ ɦɚɬɟɦɚɬɢɤɢ. |
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Ȼɟɥɨɪɭɫɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ |
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ɩɪ-ɬ ɇɟɡɚɜɢɫɢɦɨɫɬɢ, 65, ɝ. Ɇɢɧɫɤ, Ɋɟɫɩɭɛɥɢɤɚ Ȼɟɥɚɪɭɫɶ |
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Ɍɟɥ.(017)292-77-52 ɮɚɤɫ (017)292-91-37 |
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Ɋɟɝɢɫɬɪɚɰɢɨɧɧɵɣ ʋ ȻɇɌɍ/ɎɂɌɊ48-2.2011 |
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© Ⱥɧɞɪɢɹɧɱɢɤ Ⱥ.ɇ., |
Ɇɟɬɟɥɶɫɤɢɣ Ⱥ.ȼ., Ɇɢɤɭɥɢɤ ɇ.Ⱥ., Ɋɨɦɚɧɸɤ Ƚ.Ⱥ., ɘɪɢɧɨɤ ȼ.ɂ., 2011 © ȻɇɌɍ, 2011
ɋɈȾȿɊɀȺɇɂȿ |
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ȼȼȿȾȿɇɂȿ.................................................................................................................. |
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ɉɊɈȽɊȺɆɆȺ.............................................................................................................. |
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1. ɇȿɈɉɊȿȾȿɅȿɇɇɕɃ ɂɇɌȿȽɊȺɅ....................................................................... |
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1.1. ɉɨɧɹɬɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ............................................................. |
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1.2. Ɉɫɧɨɜɧɵɟ ɦɟɬɨɞɵ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ.............................................................. |
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1.2.1. ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɣ ɢ ɦɟɬɨɞ ɩɨɞɧɟɫɟɧɢɹ ɩɨɞ |
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ɡɧɚɤ ɞɢɮɮɟɪɟɧɰɢɚɥɚ ....................................................................................... |
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1.2.2. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɡɚɦɟɧɨɣ ɩɟɪɟɦɟɧɧɨɣ (ɩɨɞɫɬɚɧɨɜɤɨɣ)..................... |
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1.2.3. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɪɢ ɩɨɦɨɳɢ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɩɨɞɫɬɚɧɨɜɨɤ... |
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1.2.4. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ ɱɚɫɬɹɦ................................................................... |
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1.2.5. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɣ, ɫɨɞɟɪɠɚɳɢɯ ɤɜɚɞɪɚɬɧɵɣ ɬɪɟɯɱɥɟɧ ɜ |
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ɡɧɚɦɟɧɚɬɟɥɟ...................................................................................................... |
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1.2.6. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɪɚɰɢɨɧɚɥɶɧɵɯ ɞɪɨɛɟɣ.............................................. |
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1.2.7. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ................................ |
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1.2.8. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɢɪɪɚɰɢɨɧɚɥɶɧɵɯ ɮɭɧɤɰɢɣ....................................... |
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1.2.9. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯɪ |
ɛɢɧɨɦɨɜ.................................. |
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2. ɈɉɊȿȾȿɅȿɇɇɕɃ ɂɇɌȿȽɊȺɅ.......................................................................... |
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2.1. Ɏɨɪɦɭɥɚɇɶɸɬɨɧɚ–Ʌɟɣɛɧɢɰɚ. Ɂɚɦɟɧɚɩɟɪɟɦɟɧɧɨɣɜɨɩɪɟɞɟɥɟɧɧɨɦ |
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ɢɧɬɟɝɪɚɥɟ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟɩɨɱɚɫɬɹɦ. ȼɵɱɢɫɥɟɧɢɟɩɥɨɳɚɞɟɣɩɥɨɫɤɢɯɮɢɝɭɪ.. |
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2.2. ȼɵɱɢɫɥɟɧɢɟ ɞɥɢɧɢɞɭɝ ɤɪɢɜɵɯ. ȼɵɱɢɫɥɟɧɢɟ ɨɛɴɟɦɨɜ................................ |
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2.3. ɇɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ ............................................................................ |
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2.3.1.ɂɧɬɟɝɪɚɥɵ ɫ ɛɟɫɤɨɧɟɱɧɵɦɢ ɩɪɟɞɟɥɚɦɢ (ɧɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ |
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ɩɟɪɜɨɝɨ ɪɨɞɚ) ................................................................................................... |
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2.3.2. ɂɧɬɟɝɪɚɥɵ ɨɬ ɧɟɨɝɪɚɧɢɱɟɧɧɵɯ ɮɭɧɤɰɢɣ (ɧɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ |
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ɜɬɨɪɨɝɨ ɪɨɞɚ) ................................................................................................... |
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3.ɟɎɍɇɄɐɂɂ ɇȿɋɄɈɅɖɄɂɏ ɉȿɊȿɆȿɇɇɕɏ................................................... |
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3.1. ɉɨɧɹɬɢɟ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ ................................................ |
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3.2. ɉɪɟɞɟɥ ɢ ɧɟɩɪɟɪɵɜɧɨɫɬɶ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ.................... |
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3.3. Ⱦɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɣ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ........................... |
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3.3.1. ɑɚɫɬɧɨɟ ɢ ɩɨɥɧɨɟ ɩɪɢɪɚɳɟɧɢɹ ɮɭɧɤɰɢɢ............................................ |
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3.3.2. ɑɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ........................................................................... |
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3.3.3. ɉɨɥɧɵɣ ɞɢɮɮɟɪɟɧɰɢɚɥ ɮɭɧɤɰɢɢ ........................................................ |
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3.3.4. Ⱦɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ ɫɥɨɠɧɵɯ ɢ ɧɟɹɜɧɵɯ ɮɭɧɤɰɢɣ |
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3.4. Ʉɚɫɚɬɟɥɶɧɚɹ ɩɥɨɫɤɨɫɬɶ ɢ ɧɨɪɦɚɥɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ...................................... |
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3.5. ɗɤɫɬɪɟɦɭɦ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ............................................ |
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3.6. ɇɚɢɛɨɥɶɲɟɟ ɢ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ ɜ |
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ɡɚɦɤɧɭɬɨɣ ɨɛɥɚɫɬɢ |
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4. ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕȿ ɍɊȺȼɇȿɇɂə ɉȿɊȼɈȽɈ ɉɈɊəȾɄȺ ................... |
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4.1. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ.......... |
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4.2. Ɉɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ 1 ɩɨɪɹɞɤɚ............................. |
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4.3. Ʌɢɧɟɣɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ 1–ɝɨ ɩɨɪɹɞɤɚ........................... |
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4.4. ɍɪɚɜɧɟɧɢɹ Ȼɟɪɧɭɥɥɢ...................................................................................... |
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4.5. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜ ɩɨɥɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɚɯ...................... |
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4.6. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ |
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ɭɪɚɜɧɟɧɢɹ, ɞɨɩɭɫɤɚɸɳɢɟ ɩɨɧɢɠɟɧɢɟ ɩɨɪɹɞɤɚ................................................... |
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5. ɅɂɇȿɃɇɕȿ ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕȿ ɍɊȺȼɇȿɇɂə ȼɕɋɒɂɏ ɉɈɊəȾɄɈȼ |
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ɋ ɉɈɋɌɈəɇɇɕɆɂ ɄɈɗɎɎɂɐɂȿɇɌȺɆɂ ................................................... |
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5.1. Ʌɢɧɟɣɧɵɟ ɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ n–ɝɨ ɩɨɪɹɞɤɚ ɫ |
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ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ........................................................................... |
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5.2. Ʌɢɧɟɣɧɵɟ ɧɟɨɞɧɨɪɨɞɧɵɟɨɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɩɨɫɬɨɹɧɧɵɦɢ |
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ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ.................................................................................................... |
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6. ɅɂɇȿɃɇɕȿ ɇȿɈȾɇɈɊɈȾɇɕȿ ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕȿ ɍɊȺȼɇȿɇɂə |
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ȼɕɋɒɂɏ ɉɈɊəȾɄɈȼ ɋ ɉɈɋɌɈəɇɇɕɆɂ ɄɈɗɎɎɂɐɂȿɇɌȺɆɂ ɂ |
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ɋɉȿɐɂȺɅɖɇɈɃ ɉɊȺȼɈɃ ...............................................................ɑȺɋɌɖɘ |
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65 |
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7. ɋɂɋɌȿɆɕ ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕɏ ɍɊȺȼɇȿɇɂɃ. ɆȿɌɈȾ ɂɋɄɅɘɑȿɇɂə. |
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ɆȿɌɈȾ ɗɃɅȿɊȺ Ɋȿɒȿɇɂə ɅɂɇȿɃɇɕɏ ɋɂɋɌȿɆ ɋ ɉɈɋɌɈəɇɇɕɆɂ |
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ɟ |
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ɄɈɗɎɎɂɐɂȿɇɌȺɆɂ......................................................................................... |
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71 |
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7.1 ɇɨɪɦɚɥɶɧɚɹ ɫɢɫɬɟɦɚ n–ɝɨ ɩɨɪɹɞɤɚ ɨɛɵɤɧɨɜɟɧɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ |
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ɭɪɚɜɧɟɧɢɣ............................................................................................................... |
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71 |
7.2. Ʌɢɧɟɣɧɚɹ ɨɞɧɨɪɨɞɧɚɹ ɫɢɫɬɟɦɚ n–ɝɨ ɩɨɪɹɞɤɚ ɫ ɩɨɫɬɨɹɧɧɵɦɢ |
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ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ.................................................................................................... |
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74 |
7.3. Ɂɚɞɚɱɢɞɢɧɚɦɢɤɢ .., ɩɪɢɜɨɞɹɳɢɟɤɪɟɲɟɧɢɸɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯɭɪɚɜɧɟɧɢɣ |
78 |
4
ȼɈɉɊɈɋɕ ȾɅə ɋȺɆɈɄɈɇɌɊɈɅə...................................................................... |
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ɇɟɨɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ................................................................................... |
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82 |
Ɉɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ....................................................................................... |
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Ɏɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ....................................................................... |
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Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɢ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ... 86 |
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ɄɈɇɌɊɈɅɖɇȺə ɊȺȻɈɌȺ ʋ 2 ............................................................................... |
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ɅɂɌȿɊȺɌɍɊȺ........................................................................................................... |
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5
ȼȼȿȾȿɇɂȿ
ɇɚɫɬɨɹɳɢɟ ɦɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɢ ɤɨɧɬɪɨɥɶɧɵɟ ɪɚɛɨɬɵ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɩɟɪɜɨɝɨ ɤɭɪɫɚ ɡɚɨɱɧɨɝɨ ɨɬɞɟɥɟɧɢɹ ɢɧɠɟɧɟɪɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ ȻɇɌɍ.
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ɉɨɫɨɛɢɟ ɫɨɞɟɪɠɢɬ ɨɫɧɨɜɧɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɫɜɟɞɟɧɢɹ ɢɡ ɩɪɨɝɪɚɦɦɧɨɝɨ |
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ɦɚɬɟɪɢɚɥɚ, ɬɢɩɨɜɵɟ ɩɪɢɦɟɪɵ ɢ ɤɨɧɬɪɨɥɶɧɵɟ ɡɚɞɚɧɢɹ ɩɨ ɬɟɦɚɦ ɤɭɪɫɚ ɍɜɵɫɲɟɣ |
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ɦɚɬɟɦɚɬɢɤɢ (20 ɜɚɪɢɚɧɬɨɜ). |
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ɋɬɭɞɟɧɬ ɞɨɥɠɟɧ ɢɡɭɱɢɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ, ɪɚɡɨɛɪɚɬɶ ɩɪɢɜɟɞɟɧɧɵɟ |
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ɨɛɪɚɡɰɵ ɪɟɲɟɧɢɹ ɬɢɩɨɜɵɯ ɩɪɢɦɟɪɨɜ ɢ ɡɚɞɚɱ, ɜɵɩɨɥɧɢɬɶ |
ɪɟɲɟɧɢɟɇɡɚɞɚɱ ɫɜɨɟɝɨ |
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ɜɚɪɢɚɧɬɚ, ɧɨɦɟɪ |
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ɤɨɬɨɪɨɝɨ ɫɨɜɩɚɞɚɟɬ ɫ ɞɜɭɦɹ ɩɨɫɥɟɞɧɢɦɢ ɰɢɮɪɚɦɢ ɡɚɱɟɬɧɨɣ |
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ɤɧɢɠɤɢ (ɲɢɮɪɚ). |
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ȿɫɥɢ ɧɨɦɟɪ ɲɢɮɪɚ ɛɨɥɶɲɟ ɞɜɚɞɰɚɬɢ, ɬɨ ɫɥɟɞɭɟɬ ɨɬɧɹɬɶ ɨɬ |
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ɧɨɦɟɪɚ ɲɢɮɪɚ ɱɢɫɥɨ, ɤɪɚɬɧɨɟ 20, ɢ ɩɨɥɭɱɟɧɧɚɹ ɪɚɡɧɨɫɬɶ (ɞɜɟ ɩɨɫɥɟɞɧɢɟ ɰɢɮɪɵ) |
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ɛɭɞɟɬ ɧɨɦɟɪɨɦ ɜɚɪɢɚɧɬɚ. |
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ɇɚɩɪɢɦɟɪ: |
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ɇɨɦɟɪ ɡɚɱɟɬɧɨɣ ɤɧɢɠɤɢ |
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ɇɨɦɟɪɚ ɡɚɞɚɱ |
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ɇɨɦɟɪ ɜɚɪɢɚɧɬɚ |
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301789/148 |
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8, 28, 48 ɢ ɬ. ɞ. |
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303700/194 |
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14 |
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14, 34, 54 ɢ ɬ. ɞ. |
300120/100 |
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20 |
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20, 40, 80 ɢ ɬ. ɞ. |
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ɉɊɈȽɊȺɆɆȺ |
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Ɍɟɦɚ 1. ɇɟɨɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ |
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ɉɟɪɜɨɨɛɪɚɡɧɚɹ. ɇɟɨɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ ɢ ɟɝɨ ɫɜɨɣɫɬɜɚ. Ɍɚɛɥɢɰɚ |
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ɨɫɧɨɜɧɵɯ ɢɧɬɟɝɪɚɥɨɜ. Ɂɚɦɟɧɚ ɩɟɪɟɦɟɧɧɨɣ ɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ |
ɱɚɫɬɹɦ ɜ |
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ɧɟɨɩɪɟɞɟɥɟɧɧɨɦ ɢɧɬɟɝɪɚɥɟ. |
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ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɪɨɫɬɟɣɲɢɯ ɞɪɨɛɟɣ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɪɚɰɢɨɧɚɥɶɧɵɯ |
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ɮɭɧɤɰɢɣ. Ɇɟɬɨɞ ɪɚɰɢɨɧɚɥɢɡɚɰɢɢ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ. |
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ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɪɨɫɬɟɣɲɢɯ ɢɪɪɚɰɢɨɧɚɥɶɧɨɫɬɟɣ. |
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Ɍɟɦɚ 2. Ɉɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ |
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Ɂɚɞɚɱɢ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɨɧɹɬɢɸ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ. Ɉɩɪɟɞɟɥɟɧɧɵɣ |
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ɢɧɬɟɝɪɚɥ ɢ ɟɝɨ ɫɜɨɣɫɬɜɚ. Ɏɨɪɦɭɥɚ ɇɶɸɬɨɧɚ–Ʌɟɣɛɧɢɰɚ. |
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Ɂɚɦɟɧɚ ɩɟɪɟɦɟɧɧɨɣ ɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ ɱɚɫɬɹɦ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɢɧɬɟɝɪɚɥɟ. |
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ɇɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ. |
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ɉɪɢɥɨɠɟɧɢɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚɪɤ ɜɵɱɢɫɥɟɧɢɸ ɩɥɨɳɚɞɟɣ ɩɥɨɫɤɢɯ |
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ɮɢɝɭɪ ɜ ɞɟɤɚɪɬɨɜɵɯ ɢ ɩɨɥɹɪɧɵɯ ɤɨɨɪɞɢɧɚɬɚɯ. ȼɵɱɢɫɥɟɧɢɟ ɨɛɴɟɦɨɜ ɢ ɞɥɢɧ ɞɭɝ. |
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ɉɪɢɛɥɢɠɟɧɧɵɟ ɦɟɬɨɞɵ ɜɵɱɢɫɥɟɧɢɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ. |
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Ɍɟɦɚɢ3. Ɏɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ |
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ɨ |
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Ɏɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ. Ɉɛɥɚɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ. ɉɪɟɞɟɥ. |
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ɇɟɩɪɟɪɵɜɧɨɫɬɶ. ɑɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ. |
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ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ, |
ɩɨɥɧɵɣ |
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Ⱦɢɮɮɟɪɟɧɰɢɪɭɟɦɨɫɬɶ |
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ɞɢɮɮɟɪɟɧɰɢɚɥ. ɉɪɨɢɡɜɨɞɧɵɟ ɨɬ ɫɥɨɠɧɨɣ ɮɭɧɤɰɢɢ. ɂɧɜɚɪɢɚɧɬɧɨɫɬɶ ɮɨɪɦɵ |
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ɩɟɪɜɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɚ. ɇɟɹɜɧɵɟ ɮɭɧɤɰɢɢ ɢ ɢɯ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ. |
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Ʉɚɫɚɬɟɥɶɧɚɹ ɩɥɨɫɤɨɫɬɶ ɢ ɧɨɪɦɚɥɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. Ƚɟɨɦɟɬɪɢɱɟɫɤɢɣ ɫɦɵɫɥ ɩɨɥɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɚ ɮɭɧɤɰɢɢ ɞɜɭɯ ɩɟɪɟɦɟɧɧɵɯ. ɑɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɵ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ɏɨɪɦɭɥɚ Ɍɟɣɥɨɪɚ.
7
ɗɤɫɬɪɟɦɭɦ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ. ɇɟɨɛɯɨɞɢɦɨɟ ɢ ɞɨɫɬɚɬɨɱɧɨɟ ɭɫɥɨɜɢɹ ɷɤɫɬɪɟɦɭɦɚ. ɍɫɥɨɜɧɵɣ ɷɤɫɬɪɟɦɭɦ. Ɇɟɬɨɞ ɦɧɨɠɢɬɟɥɟɣ Ʌɚɝɪɚɧɠɚ. Ɇɟɬɨɞ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ.
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Ɂɚɞɚɱɢ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɹɦ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ |
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ɭɪɚɜɧɟɧɢɹ 1–ɝɨ ɩɨɪɹɞɤɚ. Ɂɚɞɚɱɚ Ʉɨɲɢ. Ɍɟɨɪɟɦɚ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɢ ɟɞɢɧɫɬɜɟɧɧɨɫɬɢɍ |
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ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ Ʉɨɲɢ. |
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ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ |
1–ɝɨ ɩɨɪɹɞɤɚ ɫ |
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ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ, ɨɞɧɨɪɨɞɧɵɯ, ɥɢɧɟɣɧɵɯ, ɭɪɚɜɧɟɧɢɹɇȻɟɪɧɭɥɥɢ ɢ ɜ |
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ɩɨɥɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɚɯ. |
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Ɍɟɨɪɟɦɚ |
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Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ɂɚɞɚɱɚ Ʉɨɲɢ. |
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ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɢ ɟɞɢɧɫɬɜɟɧɧɨɫɬɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ Ʉɨɲɢ. ɍɪɚɜɧɟɧɢɹ, ɞɨɩɭɫɤɚɸɳɢɟ |
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ɩɨɧɢɠɟɧɢɟ ɩɨɪɹɞɤɚ. |
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ɩɨɪɹɞɤɨɜ. |
ɋɜɨɣɫɬɜɚ |
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Ʌɢɧɟɣɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜɵɫɲɢɯ |
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ɥɢɧɟɣɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɨɩɟɪɚɬɨɪɚ. Ʌɢɧɟɣɧɨ–ɡɚɜɢɫɢɦɵɟ ɢ ɥɢɧɟɣɧɨ– |
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ɬ |
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ɧɟɡɚɜɢɫɢɦɵɟ ɫɢɫɬɟɦɵ ɮɭɧɤɰɢɣ. Ɉɩɪɟɞɟɥɢɬɟɥɶ ȼɪɨɧɫɤɨɝɨ. |
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Ʌɢɧɟɣɧɵɟ ɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ, ɭɫɥɨɜɢɟ ɥɢɧɟɣɧɨɣ |
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ɢ |
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ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɢɯ ɪɟɲɟɧɢɣ. Ɏɭɧɞɚɦɟɧɬɚɥɶɧɚɹ ɫɢɫɬɟɦɚ ɪɟɲɟɧɢɣ. ɋɬɪɭɤɬɭɪɚ |
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ɨɛɳɟɝɨ ɪɟɲɟɧɢɹ. Ʌɢɧɟɣɧɵɟ ɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ |
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ɨ |
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ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢɡ |
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ɩ |
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Ʌɢɧɟɣɧɵɟ ɧɟɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ. ɋɬɪɭɤɬɭɪɚ ɨɛɳɟɝɨ |
ɪɟɲɟɧɢɹ. Ɇɟɬɨɞ Ʌɚɝɪɚɧɠɚ ɜɚɪɢɚɰɢɢ ɩɪɨɢɡɜɨɥɶɧɵɯ ɩɨɫɬɨɹɧɧɵɯ. Ʌɢɧɟɣɧɵɟ |
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ɧɟɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɫɨ |
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ɩɪɚɜɨɣ ɱɚɫɬɶɸ. |
ɫɩɟɰɢɚɥɶɧɨɣɟ |
ɇɨɪɦɚɥɶɧɵɟ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ. Ⱥɜɬɨɧɨɦɧɵɟ ɫɢɫɬɟɦɵ. Ƚɟɨɦɟɬɪɢɱɟɫɤɢɣ ɫɦɵɫɥ ɪɟɲɟɧɢɹ. Ɏɚɡɨɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ. Ɂɚɞɚɱɢ Ʉɨɲɢ ɞɥɹ ɧɨɪɦɚɥɶɧɨɣ ɫɢɫɬɟɦɵ. Ɍɟɨɪɟɦɚ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɢ ɟɞɢɧɫɬɜɟɧɧɨɫɬɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ
8
Ʉɨɲɢ. Ɇɟɬɨɞ ɢɫɤɥɸɱɟɧɢɹ ɞɥɹ ɪɟɲɟɧɢɹ ɧɨɪɦɚɥɶɧɵɯ ɫɢɫɬɟɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ.
ɋɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɫɜɨɣɫɬɜɚ ɪɟɲɟɧɢɣ.
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Ɋɟɲɟɧɢɟ ɫɢɫɬɟɦ ɥɢɧɟɣɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɫ ɩɨɫɬɨɹɧɧɵɦɢ |
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ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ. |
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ɉɨɧɹɬɢɟ ɨ ɤɚɱɟɫɬɜɟɧɧɵɯ ɦɟɬɨɞɚɯ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɢɫɬɟɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ |
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ɭɪɚɜɧɟɧɢɣ. |
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1. ɇȿɈɉɊȿȾȿɅȿɇɇɕɃ ɂɇɌȿȽɊȺɅ |
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1.1. ɉɨɧɹɬɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ |
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Ɉɩɪɟɞɟɥɟɧɢɟ 1. Ɏɭɧɤɰɢɹ F(x) ɧɚɡɵɜɚɟɬɫɹ ɩɟɪɜɨɨɛɪɚɡɧɨɣ ɞɥɹ ɮɭɧɤɰɢɢ f(x) ɧɚ |
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ɢɧɬɟɪɜɚɥɟ (a, b), |
ɟɫɥɢ ɜɨ |
ɜɫɟɯ |
ɬɨɱɤɚɯ ɷɬɨɝɨ ɢɧɬɟɪɜɚɥɚ ɜɵɩɨɥɧɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨ |
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Fc(x)= f(x). |
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Ɉɩɪɟɞɟɥɟɧɢɟ 2. ɋɨɜɨɤɭɩɧɨɫɬɶ ɜɫɟɯɢɩɟɪɜɨɨɛɪɚɡɧɵɯ {F(x)+ɋ}, ɝɞɟ ɋ – |
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ɩɪɨɢɡɜɨɥɶɧɚɹ ɩɨɫɬɨɹɧɧɚɹ, |
ɞɥɹ ɮɭɧɤɰɢɢ f(x) ɧɚɡɵɜɚɟɬɫɹ ɧɟɨɩɪɟɞɟɥɟɧɧɵɦ |
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ɢɧɬɟɝɪɚɥɨɦ ɢ ɨɛɨɡɧɚɱɚɟɬɫɹ |
ɨ |
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³ f (x)dx F(x) C |
ɬ |
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Ɏɭɧɤɰɢɹ f(x) ɧɚɡɵɜɚɟɬɫɹ ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɣ ɮɭɧɤɰɢɟɣ, ɜɵɪɚɠɟɧɢɟ f(x) dx – |
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ɩɨɞɵɧɬɟɝɪɚɥɶɧɵɦ ɜɵɪɚɠɟɧɢɟɦɢ. |
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Ɉɬɵɫɤɚɧɢɟɡɞɥɹ ɮɭɧɤɰɢɢ f(x) ɜɫɟɯ ɟɟ ɩɟɪɜɨɨɛɪɚɡɧɵɯ F(x) + ɋ ɧɚɡɵɜɚɟɬɫɹ |
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ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɟɫɬɶ ɞɟɣɫɬɜɢɟ, ɨɛɪɚɬɧɨɟ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɸ. |
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Ɉɫɧɨɜɧɵɟ ɩɪɚɜɢɥɚ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ: |
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³df (x ) |
f (x ) C ; |
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1) |
³ f c(x )dx |
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³ f (x)dx d(F(x) C) |
f (x)dx ; |
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2) ³( f (x ) r M(x ))dx ³ f (x )dx r ³M(x )dx ; |
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³af (x )dx |
a³ f (x )dx, |
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const) ; |
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9

4) ɟɫɥɢ ³ f (x )dx |
F(x ) C , ɬɨ ³ f (ax b)dx |
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F(ax b) C , ɩɪɢ ɭɫɥɨɜɢɢ, |
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ɱɬɨ a, b – ɩɨɫɬɨɹɧɧɵɟ ɱɢɫɥɚ, az0; |
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5) ɟɫɥɢ ³ f (x )dx |
F(x ) C ɢ u=M (x) – ɥɸɛɚɹ ɞɢɮɮɟɪɟɧɰɢɪɭɟɦɚɹ ɮɭɧɤɰɢɹ, |
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ɬɨ ³ f (u)du F(u) C ; |
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Ɍɚɛɥɢɰɚ ɨɫɧɨɜɧɵɯ ɧɟɨɩɪɟɞɟɥɟɧɧɵɯ ɢɧɬɟɝɪɚɥɨɜ |
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³du |
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u C ; |
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³ |
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u |
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1. |
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10. |
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ln |
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sin u |
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D |
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uD1 |
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2. |
³ |
u du |
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C , ɝɞɟ D z 1; |
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³ |
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C ; |
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cos u |
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3. |
³ |
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u |
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ln | u | C ; |
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12. |
³ |
ɣ2 ctgu C ; |
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sin |
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4. |
³audu |
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13. |
³ |
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tgu C ; |
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ln a |
ɨ |
cos2 u |
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5. |
³eu du |
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eu C ; |
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14. |
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³ |
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arctg |
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6. |
³sin udu |
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cosu C ; |
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15. |
³ |
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arcsin |
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7. |
³cosudu ɡsin u C ; |
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16. |
³ |
du |
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³tgudu ln | cosu | C ; |
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u2 r D2 |
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8. |
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ɟ |
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ɩ |
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9. |
³ctg udu |
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ln|sin u| C ; |
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ȼ ɩɪɢɜɟɞɟɧɧɨɣ ɬɚɛɥɢɰɟ ɛɭɤɜɚ u ɦɨɠɟɬ ɨɛɨɡɧɚɱɚɬɶ ɤɚɤ ɧɟɡɚɜɢɫɢɦɭɸ |
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Ɋɩɟɪɟɦɟɧɧɭɸ, ɬɚɤ ɢ ɧɟɩɪɟɪɵɜɧɨ ɞɢɮɮɟɪɟɧɰɢɪɭɟɦɭɸ ɮɭɧɤɰɢɸ u=M(x) ɚɪɝɭɦɟɧɬɚ x. |
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