THÔNG TIN TÀI LIỆU
❚❘×❮◆● ✣❸■ ❍➴❈ ❙× P❍❸▼ ❍⑨ ◆❐■ ✷ ❑❍❖❆ ❚❖⑩◆ ✖✖✖✖✕♦✵♦✖✖✖✖✖ ◆●❯❨➍◆ ❚❍➚ ❍⑨ ❇❷◆● ❚➐▼ ❑■➌▼ ✭▲❖❖❑❯P ❚❆❇▲❊✮ ❱⑨ Ù◆● ❉Ö◆● ❑❍➶❆ ▲❯❾◆ ❚➮❚ ◆●❍■➏P ✣❸■ ❍➴❈ ❈❤✉②➯♥ ♥❣➔♥❤✿ ❚♦→♥ ù♥❣ ❞ư♥❣ ❍⑨ ◆❐■✲✷✵✶✾ ❚❘×❮◆● ✣❸■ ❍➴❈ ❙× P❍❸▼ ❍⑨ ◆❐■ ✷ ❑❍❖❆ ❚❖⑩◆ ✖✖✖✖✕♦✵♦✖✖✖✖✖ ◆●❯❨➍◆ ❚❍➚ ❍⑨ ❇❷◆● ❚➐▼ ❑■➌▼ ✭▲❖❖❑❯P ❚❆❇▲❊✮ ❱⑨ Ù◆● ❉Ö◆● ❑❍➶❆ ▲❯❾◆ ❚➮❚ P ự ữớ ữợ ❞➝♥ ❦❤♦❛ ❤å❝ ❚❤✳❙ ❚r➛♥ ❚✉➜♥ ❱✐♥❤ ❍⑨ ◆❐■✲✷✵✶✾ ▲í✐ ❝↔♠ ì♥ ✣➸ ❤♦➔♥ t❤➔♥❤ q✉→ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ✈➔ ❤♦➔♥ t❤✐➺♥ ❦❤â❛ ❧✉➟♥ ♥➔②✱ ❧í✐ ✤➛✉ t✐➯♥✱ tỉ✐ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ tỵ✐ ❝→❝ t❤➛② ❝ỉ tr♦♥❣ ❦❤♦❛ ❚♦→♥✱ ❝→❝ t❤➛② ❝ỉ tr♦♥❣ tê Ù♥❣ ❞ư♥❣ ✤➣ ❞↕② ❞é tỉ✐ t➟♥ t➻♥❤ tr♦♥❣ s✉èt t❤í✐ ❣✐❛♥ tỉ✐ ❤å❝ t➟♣ t↕✐ tr÷í♥❣ ✣❍❙P ❍➔ ◆ë✐ ✷✳ ❚ỉ✐ ①✐♥ ❣û✐ ❧í✐ ❝↔♠ ì♥ s➙✉ s➢❝ ♥❤➜t tỵ✐ t❤➛② ❣✐→♦ ❱✐♥❤✳ ❚❤❙✳ ❚r➛♥ ❚✉➜♥ ❚❤➛② ❧➔ ♥❣÷í✐ ✤➣ ❣✐↔♥❣ ❞↕② ♥❤ú♥❣ tự t t t ú ù ữợ ❝❤➾ ❜↔♦ tỉ✐ tr♦♥❣ s✉èt t❤í✐ ❣✐❛♥ tỉ✐ t❤ü❝ ❤✐➺♥ ❦❤â❛ ❧✉➟♥ tèt ♥❣❤✐➺♣ ♥➔②✳ ▼ët ❧➛♥ ♥ú❛ tæ✐ ①✐♥ t ỡ t ú t ỗ sù❝ ❦❤ä❡✳ ❚✉② ♥❤✐➯♥✱ ❞♦ ✤➙② ❧➔ ❧➛♥ ✤➛✉ t✐➯♥ tỉ✐ ❧➔♠ q✉❡♥ ✈ỵ✐ ❝ỉ♥❣ ✈✐➺❝ ♥❣❤✐➯♥ ❝ù✉ ❦❤♦❛ ❤å❝✱ ❤ì♥ ♥ú❛ ❞♦ t❤í✐ ❣✐❛♥ ✈➔ ♥➠♥❣ ❧ü❝ ❝õ❛ ❜↔♥ t❤➙♥ ❝á♥ ❤↕♥ ❝❤➳ ♥➯♥ ❦❤æ♥❣ t❤➸ tr→♥❤ ❦❤ä✐ ♥❤ú♥❣ t❤✐➳✉ sât✳ ❱➻ ✈➟② tỉ✐ ❦➼♥❤ ♠♦♥❣ ♥❤➟♥ ✤÷đ❝ sü õ õ ỵ qỵ t ổ ✈➔ ❝→❝ ❜↕♥ s✐♥❤ ✈✐➯♥ ✤➸ ❦❤â❛ ❧✉➟♥ ❝õ❛ tæ✐ ✤÷đ❝ ❤♦➔♥ t❤✐➺♥ ❤ì♥✳ ❚ỉ✐ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥✦ ❍➔ ◆ë✐✱ t❤→♥❣ ✺ ♥➠♠ ✷✵✶✾ ❙✐♥❤ ✈✐➯♥ ◆❣✉②➵♥ ❚❤à ❍➔ ✶ ▲í✐ ❝❛♠ ✤♦❛♥ ❚ỉ✐ ①✐♥ ❦❤➥♥❣ ✤à♥❤ ✤➙② ❧➔ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ ❝õ❛ r✐➯♥❣ ❝→ ♥❤➙♥ tæ✐ ợ sỹ ữợ t r ❱✐♥❤✳ ✣➲ t➔✐ ♥➔② ❝❤÷❛ tø♥❣ ✤÷đ❝ ❝ỉ♥❣ ❜è ð ✤➙✉ ✈➔ ❤♦➔♥ t♦➔♥ ❦❤ỉ♥❣ trò♥❣ ✈ỵ✐ ♥❣❤✐➯♥ ❝ù✉ ❝õ❛ t→❝ ❣✐↔ ❦❤→❝✳ ✷ ▼ư❝ ❧ư❝ ▲í✐ ❝↔♠ ì♥ ✶ ▲í✐ ❝❛♠ ✤♦❛♥ ✷ ▼ð ✤➛✉ ✻ ✶ ❚✃◆● ◗❯❆◆ ❱➋ ❇❷◆● ❚➐▼ ❑■➌▼ ✾ ✶✳✶ ❇↔♥❣ t➻♠ ❦✐➳♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✶✳✷ ▲à❝❤ sû ♥❣❤✐➯♥ ❝ù✉ ✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ❇❷◆● ❚➐▼ ❑■➌▼ ❱⑨ ◆❐■ ❙❯❨ ❚❯❨➌◆ ❚➑◆❍ ❚❘❖◆● ❇❷◆● ❚➐▼ ❑■➌▼ ✶✶ ✷✳✶ ❱➼ ❞ö ✤ì♥ ❣✐↔♥ ✈➲ ❜↔♥❣ t➻♠ ❦✐➳♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷ P❤÷ì♥❣ ♣❤→♣ ♥ë✐ s✉② sû ❞ư♥❣ tr♦♥❣ ❜↔♥❣ t➻♠ ❦✐➳♠ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✸ ❙û ❞ư♥❣ ♣❤÷ì♥❣ ♣❤→♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❜↔♥❣ t➻♠ ❦✐➳♠ ✶✸ ✷✳✸✳✶✳ ❈➜✉ tró❝ ❝õ❛ ❜↔♥❣ t➻♠ ❦✐➳♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✸✳✷✳ ❇↔♥❣ t➻♠ ❦✐➳♠ ♠ët ❝❤✐➲✉ ✈➔ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ♠ët ❝❤✐➲✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✸✳✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ❚ê♥❣ q✉→t ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ♥ ❝❤✐➲✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ Ù◆● ❉Ö◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ✸✳✶ ✶✼ ❇↔♥❣ t➻♠ ❦✐➳♠ ❜❛ ❝❤✐➲✉ ✈➔ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❜❛ ❝❤✐➲✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✸✳✺✳ ✶✺ ❇↔♥❣ t➻♠ ❦✐➳♠ ❤❛✐ ❝❤✐➲✉ ✈➔ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❤❛✐ ❝❤✐➲✉ ✷✳✸✳✹✳ ✶✸ ✷✺ ✷✻ ❙û ❞ư♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ♠ët ❝❤✐➲✉ ✤➸ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✷✼ ✸✳✷ ❙û ❞ư♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ❤❛✐ ❝❤✐➲✉ ✤➸ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✸ ✷✾ ❙û ❞ö♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❜❛ ❝❤✐➲✉ ✤➸ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ❑➳t ❧✉➟♥ ✸✹ ❚⑨■ ▲■➏❯ ❚❍❆▼ ❑❍❷❖ ✸✺ ✹ ❉❛♥❤ s→❝❤ ❜↔♥❣ y = x3 ✳ ✳ ✳ ✳ ✳ trà ❤➔♠ y = x t↕✐ ✷✳✶ ❇↔♥❣ ❜✐➸✉ ❞✐➵♥ ❤➔♠ ✳ ✳ ✳ ✳ ✳ ✳ ữợ t➼♥❤ ❣✐→ ✤✐➸♠ ✳ ✳ ✳ ✳ ✶✷ ✷✳✸ ❇↔♥❣ ✤♦ ♥❤✐➺t ✤ë t↕✐ ♥❤➔ ◆❛♠ ❜✉ê✐ tr÷❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✹ ❇↔♥❣ ♠✐♥❤ ❤å❛ ❝➜✉ tró❝ ❝õ❛ ❜↔♥❣ t➻♠ ❦✐➳♠ ❤❛✐ ❝❤✐➲✉ ✳ ✳ ✳ ✳ ✶✹ ✷✳✺ ❇↔♥❣ t➻♠ ❦✐➳♠ ❤❛✐ ❝❤✐➲✉ ♠æ t↔ ♠ët ❤➔♠ ❜✐➸✉ t❤à t❤❡♦ ❤❛✐ ❜✐➳♥ ❝❤✐➲✉ ❝❛♦ ✈➔ ❝➙♥ ♥➦♥❣ sinx x = −1, ✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ t↕✐ ❝→❝ ✤✐➸♠ ✤➦❝ ❜✐➺t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✻ ●✐→ trà ❤➔♠ ✸✳✶ ❇↔♥❣ ❝❤ù❛ t✛ ❧➺ P❉(%) ✈➔ t✛ ❧➺ ❊❈(%) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✷ ❇↔♥❣ ❝❤ù❛ ❦➻ ❤↕♥ ✭♥➠♠✮✱ t÷ì♥❣ q✉❛♥(%) ✈➔ t✛ ❧➺ ❊❈(%) ✳ ✳ ✷✾ ✸✳✸ ❇↔♥❣ ❝❤ù❛ ❦➻ ❤↕♥ ✭♥➠♠✮✱ t÷ì♥❣ q✉❛♥ ❧➺ ❊❈ (%) (%)✱ ▲●❉ (%) ✈➔ t✛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✸✶ ❉❛♥❤ s→❝❤ ❤➻♥❤ ✈➩ ỗ t t t❤í✐ ✤✐➸♠ ✶✷❤ tr÷❛ ✶✸ ✷✳✷ ◆ë✐ s✉② t✉②➳♥ t➼♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✸ ◆ë✐ s✉② s♦♥❣ t✉②➳♥ t➼♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✹ ❍➻♥❤ ✈➩ ♠æ t↔ ❜è♥ ✤✐➸♠ ↔♥❤ ✤➣ ❜✐➳t ✈➔ ✤✐➸♠ ↔♥❤ ❝➛♥ ♥ë✐ s✉②✳ ✷✵ ✷✳✺ ◆ë✐ s✉② t❛♠ t✉②➳♥ t➼♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✻ ❍➻♥❤ ♠✐♥❤ ❤å❛ ❣✐→ trà ✤✐➸♠ ♥ë✐ s✉② ✸✳✶ ❍➻♥❤ ♠✐♥❤ ❤å❛ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ✸✳✷ ▼æ ♣❤ä♥❣ t✛ ❧➺ ❊❈ ❝➛♥ ♥ë✐ s✉② tr♦♥❣ ✤♦↕♥ ❆❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✸ ❚✛ ❧➺ ❊❈ ❝➛♥ ♥ë✐ s✉② tr♦♥❣ ❤➻♥❤ ❝❤ú ♥❤➟t ❆❇❈❉ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✹ ▼æ ♣❤ä♥❣ t✛ ❧➺ ❊❈ ❝➛♥ ♥ë✐ s✉② tr♦♥❣ ❧➠♥❣ trö ❆❇❈❉❊❋●❍ ✸✷ ✻ p = f (0, 9; 0, 9; 0, 9) ✷✶ ✳ ✳ ✷✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỵ ❝❤å♥ ✤➲ t➔✐ ❇↔♥❣ t➻♠ ❦✐➳♠ ✤➣ ✈➔ ✤❛♥❣ ✤÷đ❝ ù♥❣ ❞ö♥❣ r➜t ♥❤✐➲✉ ✈➔♦ ❝→❝ ♥❣➔♥❤ ❝õ❛ ❦❤♦❛ ❤å❝ ✈➔ ❦ÿ t❤✉➟t ❦❤→❝ ♥❤❛✉✳ ❚❤í✐ ❣✐❛♥ ❣➛♥ ✤➙② sü ♣❤→t tr✐➸♥ ❝õ❛ ❦❤♦❛ ❤å❝ ♠→② t➼♥❤ ✤➣ ♠ð r❛ ởt ữớ ợ tr ổ tt ♥➠♥❣ ✈➔ tè❝ ✤ë ❝õ❛ ♠→② t➼♥❤ ✤÷đ❝ ❝↔✐ t❤✐➺♥ t ỷ ỵ t ỵ tt ự t trữợ ✤➙② ❝❤÷❛ ✤÷đ❝ ❣✐↔✐ q✉②➳t✳ ❈❤➼♥❤ ✈➻ t❤➳ ❜↔♥❣ t➻♠ ữủ sỹ ú ỵ s ✈✐➯♥ ❙÷ ♣❤↕♠ ❚♦→♥ ❤å❝ ♥â✐ ❝❤✉♥❣ ❝❤÷❛ ❝â ♥❤✐➲✉ ✤✐➲✉ ❦✐➺♥ ✤➸ t➻♠ ❤✐➸✉ ✈➲ ❜↔♥❣ t➻♠ ❦✐➳♠ ✈➔ ù♥❣ ❞ư♥❣ ❝õ❛ ❜↔♥❣ t➻♠ ❦✐➳♠✳ ❱➻ ✈➟② tỉ✐ ❝❤å♥ ✤➲ t➔✐ ✏❇↔♥❣ t➻♠ ❦✐➳♠ ✈➔ ù♥❣ ❞ö♥❣✑ ❧➔♠ ❦❤â❛ ❧✉➟♥ tèt ♥❣❤✐➺♣ ♥❤➡♠ ✤÷❛ r❛ ♠ët sè ❧➼ t❤✉②➳t ❝ì ❜↔♥ ✈➲ ❜↔♥❣ t➻♠ ❦✐➳♠✱ ♣❤÷ì♥❣ ♣❤→♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ ✤÷đ❝ sû ❞ư♥❣ tr♦♥❣ ❜↔♥❣ t➻♠ ❦✐➳♠ ✈➔ ♠ët ✈➔✐ ù♥❣ ❞ö♥❣ ❝ö t❤➸ ❝õ❛ ❜↔♥❣ t➻♠ ❦✐➳♠ ✈➔♦ ❝→❝ ♥❣➔♥❤ ❦❤♦❛ ❤å❝✳ ■■✳ ▼ö❝ t✐➯✉ ♥❣❤✐➯♥ ❝ù✉ ▼ö❝ t✐➯✉ ❝õ❛ ❦❤â❛ ❧✉➟♥ ❧➔ t➻♠ ❤✐➸✉ ✈➲ ❜↔♥❣ t➻♠ ❦✐➳♠ ✈➔ tø ✤â ✤÷❛ r❛ ❝→❝ ù♥❣ ❞ư♥❣ ❝ö t❤➸ ❝õ❛ ❜↔♥❣ t➻♠ ❦✐➳♠ tr♦♥❣ t♦→♥ ❤å❝ ✈➔ tr♦♥❣ t❤ü❝ t➳✳ ■■■✳ ◆❤✐➺♠ ✈ö ♥❣❤✐➯♥ ❝ù✉ ◆❣❤✐➯♥ ❝ù✉ ❝ì sð ❧➼ ❧✉➟♥ ✈➲ ❜↔♥❣ t➻♠ ❦✐➳♠✳ ◆❣❤✐➯♥ ❝ù✉ ❝ì sð ❧➼ ❧✉➟♥ ✈➲ ♣❤÷ì♥❣ ♣❤→♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ ✤÷đ❝ sû ❞ư♥❣ tr♦♥❣ ❜↔♥❣ t➻♠ ❦✐➳♠✳ ✣÷❛ r❛ ù♥❣ ❞ö♥❣ ❝ö t❤➸ ❝õ❛ ❜↔♥❣ t➻♠ ❦✐➳♠✳ ■❱✳ ❈➜✉ tró❝ ❦❤â❛ ❧✉➟♥ ✼ ✽ ◆❣♦➔✐ ♣❤➛♥ ♠ð ✤➛✉✱ ❦➳t t t õ ỗ ❝❤÷ì♥❣✿ ❈❤÷ì♥❣ ✶✿ ❚ê♥❣ q✉❛♥ ✈➲ ❜↔♥❣ t➻♠ ❦✐➳♠ ❈❤÷ì♥❣ ✷✿ ❇↔♥❣ t➻♠ ❦✐➳♠ ✈➔ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❜↔♥❣ t➻♠ ❦✐➳♠ ❈❤÷ì♥❣ ✸✿ ù♥❣ ❞ư♥❣ ❝õ❛ ❜↔♥❣ t➻♠ ❦✐➳♠ ❈❤÷ì♥❣ ✷✳ ❑■➌▼ p1 ❇❷◆● ❚➐▼ ❑■➌▼ ❱⑨ ◆❐■ ❙❯❨ ❚❯❨➌◆ ❚➑◆❍ ❚❘❖◆● ❇❷◆● ❚➐▼ ✷✶ ♥❤÷ tr♦♥❣ ♥ë✐ s✉② s♦♥❣ t✉②➳♥ t➼♥❤ ✷❉✱ s❛✉ ✤â t❤➯♠ ♠ët ❧➛♥ ♥ú❛ ✤➸ t➼♥❤ [1] t♦→♥ ✤✐➸♠ ♣✳ ❍➻♥❤ ✷✳✺✿ ◆ë✐ s✉② t❛♠ t✉②➳♥ t➼♥❤ ✣➸ t❤✉ ✤÷đ❝ ❣✐→ trà ❝❤♦ ✤✐➸♠ p00 ✱ ù♥❣ ❞ö♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr➯♥ ✤✐➸♠ p00 = p000 + ❚÷ì♥❣ tü✱ t➻♠ ✤✐➸♠ p000 ✈➔ p100 ✤➸ ✤↕t x − x0 (p100 − p000 ) x1 − x0 p10 ✱ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr➯♥ ✤✐➸♠ p010 p10 = p010 + y0 ✈➔ ✤÷đ❝ p00 ✳ ✤➛✉ t✐➯♥ t❛ ❣✐ú ♥❣✉②➯♥ ❤➡♥❣ sè ✈➔ p110 t❛ ✤÷đ❝✿ x − x0 (p110 − p010 ) x1 − x0 ◆ë✐ s✉② t✉②➳♥ t➼♥❤ ❧➛♥ t❤ù ✸ ❜➡♥❣ ❝→❝❤ ❣✐ú ♥❣✉②➯♥ ❤➡♥❣ sè ①✱ ù♥❣ ❞ö♥❣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr➯♥ ❤❛✐ ✤✐➸♠ p0 = p00 + p10 ✈➔ p00 ✤➸ t➻♠ r❛ ✤✐➸♠ y − y0 (p10 − p00 ) y1 − y0 p0 ✳ ❈❤÷ì♥❣ ✷✳ ❑■➌▼ ❇❷◆● ❚➐▼ ❑■➌▼ ❱⑨ ◆❐■ ❙❯❨ ❚❯❨➌◆ ❚➑◆❍ ❚❘❖◆● ❇❷◆● ❚➐▼ ❇➡♥❣ ❝→❝❤ ❧➔♠ t÷ì♥❣ tü✱ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ ✸ ❧➛♥ t➻♠ r❛ ✤✐➸♠ ✷✷ p1 ✳ x − x0 (p101 − p001 ) x1 − x0 x − x0 p11 = p011 + (p111 − p011 ) x1 − x0 y − y0 p1 = p01 + (p11 − p01 ) y1 − y0 p01 = p001 + ❚ø ❤❛✐ ✤✐➸♠ p0 ✈➔ t➼♥❤ tr➯♥ ❤❛✐ ✤✐➸♠ p1 ✱ ❜➡♥❣ ❝→❝❤ ❣✐ú ♥❣✉②➯♥ ②✱ ù♥❣ ❞ư♥❣ ♥ë✐ s✉② t✉②➳♥ p0 ✈➔ p1 t❛ t➻♠ ✤÷đ❝ ✤✐➸♠ ♣ ❝➛♥ t➻♠ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ✸❉ p = p0 + z − z0 (p1 − p0 ) z1 − z0 ❚❤❛② ❣✐→ trà tê♥❣ q✉→t ❝õ❛ ❝→❝ ❜✐➸✉ t❤ù❝ p00 ✱ p01 ✱ p10 ✱ p11 ✱p0 ✱p1 ✈➔♦ ♣ t❛ ✤÷đ❝ ❜✐➸✉ t❤ù❝ tê♥❣ q✉→t ❝❤♦ ♣❤➨♣ ♥ë✐ s✉② t❛♠ t✉②➳♥ ✤÷đ❝ ✤÷❛ r❛ tr♦♥❣ ♣❤÷ì♥❣ tr➻♥❤ ✭✷✳✺✮ p = c0 +c1 ∆x+c2 ∆y +c3 ∆z +c4 ∆x∆y +c5 ∆y∆z +c6 ∆z∆x+c7 ∆x∆y∆z tr♦♥❣ ✤â ∆x❀ ∆y ✱ ∆z ❧➔ ❦❤♦↔♥❣ ❝→❝❤ t÷ì♥❣ ✤è✐ ❝õ❛ ❝→❝ ✤✐➸♠ ố ợ t t p000 t ữợ ②✱ ③ t÷ì♥❣ ù♥❣✱ ✤÷đ❝ ❜✐➸✉ t❤à tr♦♥❣ ♣❤÷ì♥❣ tr➻♥❤ ✭✷✳✺✮ ∆x = ❍➺ sè c0 c1 c2 c3 c4 c5 c6 c7 cj x − x0 y − y0 z − z0 , ∆y = , ∆z = x1 − x0 y − y0 z1 − z0 ✤÷đ❝ ①→❝ ✤à♥❤ tø ❣✐→ trà ❝õ❛ ❝→❝ ✤➾♥❤ = p000 ; = p100 − p000 ; = p010 − p000 ; = p001 − p000 ; = p110 − p010 − p100 + p000 ; = p011 − p001 − p010 + p000 ; = p101 − p001 − p100 + p000 = p111 − p011 − p101 − p110 + p100 + p001 + p010 − p000 ▼ët ❝→❝❤ ♥❤➻♥ ❦❤→❝ ❧➠♥❣ trư ❆❇❈❉❊❋●❍ ✤÷đ❝ ♣❤➙♥ ❤♦↕❝❤ t❤➔♥❤ t→♠ ❦❤è✐ ❜ð✐ ❝→❝ ♠➦t ♣❤➥♥❣ ①✱ ② ✈➔ ③✳ ✣➸ ♥ë✐ s✉② ❣✐→ trà ♣ ❝❤♦ ❜ð✐ ❤➔♠ p = f (x, y, z) t↕✐ ✤✐➸♠ ■ ✤➛✉ t✐➯♥ ❝❤ó♥❣ t❛ t➻♠ ✈ò♥❣ ❝❤✉➞♥ ❤â❛ ❝õ❛ ❧➠♥❣ ❦➼♥❤ ❆❇❈❉❊❋●❍✳ ❚→♠ t➟♣ ✤÷đ❝ ❝❤✉➞♥ ❤â❛ ❜➡♥❣ ❝→❝❤ ❝❤✐❛ ❈❤÷ì♥❣ ✷✳ ❑■➌▼ ❇❷◆● ❚➐▼ ❑■➌▼ ❱⑨ ◆❐■ ❙❯❨ ❚❯❨➌◆ ❚➑◆❍ ❚❘❖◆● ❇❷◆● ❚➐▼ ❝❤ó♥❣ ❝❤♦ ❦❤è✐ ❧÷đ♥❣ ❧➠♥❣ ❦➼♥❤ ❆❇❈❉❊❋●❍✳ Na , Nb , Nc , Nd , Ne , Nf , Ng , Nh Na = [2] ✷✸ ❚→♠ ✈ò♥❣ ❝❤✉➞♥ ❤â❛ ✤÷đ❝ t➼♥❤ t❤❡♦ ❝ỉ♥❣ t❤ù❝✿ (x1 − x)(y1 − y)(z − z0 ) (x1 − x)(y − y0 )(z − z0 ) ; Nb = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x − x0 )(y1 − y)(z − z0 ) ; Nd = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x)(y1 − y)(z1 − z) Ne = ; Nf = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x − x0 )(y1 − y)(z1 − z) ; Nh = Ng = (x1 − x0 )(y1 − y0 )(z1 − z0 ) Nc = (x − x0 )(y − y0 )(z − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x)(y − y0 )(z1 − z) (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x − x0 )(y − y0 )(z1 − z) (x1 − x0 )(y1 − y0 )(z1 − z0 ) ❑❤✐ ✤â ♣❤÷ì♥❣ tr➻♥❤ ✭✷✳✺✮ ❝á♥ ✤÷đ❝ t ữợ ữỡ tr ữ s p = p001 Na +p011 Nb +p101 Nc +p111 Nd +p000 Ne +p010 Nf +p100 Ng +p110 Nh ❱➼ ❞ö✿ ❈❤♦ ❤➔♠ sè p = f (x, y, z) ✈ỵ✐ ♠ët sè ỳ t tr ữợ ① ② ③ p = f (x, y, z) ✵ ✵ ✵ ✵ ✵ ✵ ✶ ✷ ✵ ✶ ✵ ✹ ✵ ✶ ✶ ✻ ✶ ✵ ✵ ✶ ✶ ✵ ✶ ✸ ✶ ✶ ✵ ✺ ✶ ✶ ✶ ✼ p = f (0, 9; 0, 9; 0, 9) ❜↔♥❣ ✭✷✳✼✮ t❛ ❝â x0 = 0; x1 = 1; y0 = 0; y1 = 1; ❚➼♥❤ ❣✐→ trà ❤➔♠ ❉ü❛ ✈➔♦ sè ❧✐➺✉ z0 = 0; z1 = [0, 1] ♥➯♥ t❛ ❝â t❤➸ →♣ ❞ö♥❣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ ❝õ❛ ❤➔♠ f (0, 9; 0, 9; 0, 9)✳ ●✐→ trà ✵✱✾ ♥➡♠ tr♦♥❣ ✤♦↕♥ ✤➸ t➻♠ r❛ ❣✐→ trà ①➜♣ ①➾ ❈❤÷ì♥❣ ✷✳ ❑■➌▼ ❇❷◆● ❚➐▼ ❑■➌▼ ❱⑨ ◆❐■ ❙❯❨ ❚❯❨➌◆ ❚➑◆❍ ❚❘❖◆● ❇❷◆● ❚➐▼ ✷✹ ❍➻♥❤ ✷✳✻✿ ❍➻♥❤ ♠✐♥❤ ❤å❛ ❣✐→ trà ✤✐➸♠ ♥ë✐ s✉② p = f (0, 9; 0, 9; 0, 9) ❈→❝ ♠➦t ♣❤➥♥❣ x = 0, 9; y = 0, 9; z = 0, ❝❤✐❛ ❧➠♥❣ ❦➼♥❤ t❤➔♥❤ t→♠ ♣❤➙♥ ✈ò♥❣ ✤÷đ❝ ❝❤♦ ❜ð✐ ❝ỉ♥❣ t❤ù❝✿ Na = (x1 − x)(y1 − y)(z − z0 ) (x1 − x)(y − y0 )(z − z0 ) ; Nb = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) Nc = (x − x0 )(y1 − y)(z − z0 ) (x − x0 )(y − y0 )(z − z0 ) ; Nd = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) Ne = (x1 − x)(y1 − y)(z1 − z) (x1 − x)(y − y0 )(z1 − z) ; Nf = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) Ng = (x − x0 )(y − y0 )(z1 − z) (x − x0 )(y1 − y)(z1 − z) ; Nh = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) p = 2.Na + 6.Nb + 3.Nc + 7.Nd + 0.Ne + 4.Nf + 1.Ng + 5.Nh ❚❤❛② x0 = 0; x1 = 1; y0 = 0; y1 = 1; z0 = 0; z1 = 1; x = 0, 9; y = 0, 9; z = 0, ✈➔♦ Na , Nb , Nc , Nd , Ne , Nf , Ng , Nh ❙✉② r❛ p = f (0, 9; 0, 9; 0, 9) = 6, 3✳ ❑❤✐ ✤â✿ ❈❤÷ì♥❣ ✷✳ ❑■➌▼ ❇❷◆● ❚➐▼ ❑■➌▼ ❱⑨ ◆❐■ ❙❯❨ ❚❯❨➌◆ ❚➑◆❍ ❚❘❖◆● ❇❷◆● ❚➐▼ ✷✺ ✷✳✸✳✺✳ ❚ê♥❣ q✉→t ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ♥ ❝❤✐➲✉ ◆ë✐ s✉② t✉②➳♥ t➼♥❤ ð sè ❝❤✐➲✉ ❧ỵ♥ ❤ì♥✱ ❝→❝ ♥❣✉②➯♥ t➢❝ t÷ì♥❣ tü ❝ơ♥❣ ✤÷đ❝ →♣ ❞ư♥❣✳ ●✐↔ sû ❝❤ó♥❣ t❛ ❝â ❤➔♠ ❣➛♥ ♥❤÷ ❝❤➼♥❤ ①→❝ ❤♦➦❝ t✉②➳♥ t➼♥❤ y = f (x1 , x2 , , xn ) ❱➔ t❛ ❝â n ❝❤♦ ♠ët ✤✐➸♠ ✤✐➸♠ ❧➔ ✤➾♥❤ ❝õ❛ ♠ët ✤❛ ❞✐➺♥ ❤➻♥❤ ❝❤ú ♥❤➟t✳ ◆➳✉ t❛ ✤÷đ❝ (x1 , x2 , , xn ) tr♦♥❣ ♣❤➛♥ ❜➯♥ tr♦♥❣ ❝õ❛ ❤➻♥❤ ✤❛ ❞✐➺♥✱ t❤➻ ❤➻♥❤ ✤❛ ❞✐➺♥ ✤÷đ❝ ❝❤✐❛ t❤➔♥❤ 2n ♣❤➙♥ ✈ò♥❣ ❜ð✐ ♥ ❝❤✐➲✉ ✤✐ q✉❛ ✤✐➸♠ ♥ë✐ [2] s✉② ▼é✐ ♣❤➙♥ ✈ò♥❣ ❝â ♠ët sè ❧÷đ♥❣ ❝❤✉➞♥ ❤â❛ ✤÷đ❝ ❝❤♦ ❜ð✐✿ N00 = (x11 − x12 )(x21 − x22 ) (xn1 − xn2 ) (x11 − x10 )(x21 − x20 ) (xn1 − xn0 ) N00 = (x11 − x12 )(x21 − x22 ) (xn2 − xn0 ) (x11 − x10 )(x21 − x20 ) (xn1 − xn0 ) ✳✳✳ N11 = (x12 − x10 )(x22 − x20 ) (xn2 − xn0 ) (x11 − x10 )(x21 − x20 ) (xn1 − xn0 ) (x10 , x20 , xn0 ) ❧➔ ✤➾♥❤ ❝õ❛ ❤➻♥❤ ✤❛ ❞✐➺♥ (x11 , x21 , xn1 ) ❧➔ ✤➾♥❤ ①❛ ♥❤➜t tø ❣è❝✳ ●✐→ trà ② ❚r♦♥❣ ✤â ✤✐➸♠ ✈➔ ✤✐➸♠ s✉② tr♦♥❣ ❤➻♥❤ ✤❛ ❞✐➺♥ ✤÷đ❝ ✤÷❛ r❛ ❜ð✐✿ y = x1 N1 + x2 N2 + + xn Nn ❣➛♥ ✤✐➸♠ ❣è❝ ❝õ❛ ✤✐➸♠ ♥ë✐ ❈❤÷ì♥❣ ✸ Ù◆● ❉Ư◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ❙û ❞ö♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ ✤❛ ❝❤✐➲✉ ✤➸ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳✳ ❚r♦♥❣ ♥❣➙♥ ❤➔♥❣✱ ❱è♥ ❦✐♥❤ t➳ ✭❊❈ ✲ ❊❝♦♥♦♠✐❝ ❈❛♣✐t❛❧✮ ❧➔ sè ố rừ r ữợ t tr➻ ♠ù❝ ✤ë t✐♥ t÷ð♥❣ ð ♠ët ♠ù❝ ✤ë t✐♥ ❝➟② ♥❤➜t ✤à♥❤ ✈➔ ❦❤♦↔♥❣ t❤í✐ ❣✐❛♥ ♥❤➜t ✤à♥❤✳ ◆â ❝✉♥❣ ❝➜♣ ♠ët ❝ì sð ❝❤✉♥❣ ✤➸ s♦ s→♥❤ ❧đ✐ ♥❤✉➟♥ ✤÷đ❝ ✤✐➲✉ ❝❤➾♥❤ t❤❡♦ rõ✐ r♦ ✈➔ ❣✐→ trà ❦✐♥❤ t➳ t÷ì♥❣ ✤è✐ ❝õ❛ ❝→❝ ♥❣➔♥❤ ❦✐♥❤ ❞♦❛♥❤ ✈➔ t s ợ ự ỗ rừ r õ ự ỗ ✤♦ ❧÷í♥❣ ❤✐➺✉ s✉➜t✱ ✤à♥❤ ❣✐→ ✤✐➲✉ ❝❤➾♥❤ rõ✐ r♦✱ ố t ố q ỵ t tr✉♥❣ rõ✐ r♦✳ ❊❈ ❝â t❤➸ ✤÷đ❝ ♣❤➙♥ ❜ê ð ♠ù❝ ❝❤♦ ✈❛②✱ ❝ì sð ❤♦➦❝ ♥❣➔♥❤ ♥❣❤➲ ð ❝➜♣ ✤ë ❦✐♥❤ ❞♦❛♥❤✳ ✣➸ ❝✉♥❣ ❝➜♣ ♠ët ♣❤÷ì♥❣ ♣❤→♣ ✤➸ t➼♥❤ t♦→♥ ❊❈✱ ♥❣÷í✐ t❛ sû ❞ư♥❣ ❝→❝ ❣✐→ trà ✤➛✉ ✈➔♦ ❦❤→❝ ♥❤❛✉ ♥❤÷✿ ①→❝ ①✉➜t ♠➦❝ ✤à♥❤ ❝õ❛ tø♥❣ ❦❤♦↔♥ ✈❛② ✭P❉ ✲ Pr♦❜❛❜✐❧✐t② ♦❢ ❉❡❢❛✉❧t✮✱ ▲●❉ ✭▲♦ss ●✐✈❡♥ ❉❡❢❛✉❧t✮✱ ♠è✐ t÷ì♥❣ q✉❛♥ ✭❈♦rr❡❧❛t✐♦♥✮ ❣✐ú❛ ♥❤ú♥❣ ♥❣÷í✐ ✈❛② ❦❤→❝ ♥❤❛✉ tr♦♥❣ ❞❛♥❤ ♠ư❝ ✤➛✉ t÷✱ t❤í✐ ❤↕♥ ❝á♥ ❧↕✐ ❝õ❛ ❦❤♦↔♥ ✈❛② ✭▼❛t✉r✐t②✮✱✳✳✳ ❈→❝❤ t✐➳♣ ❝➟♥ ♥➔② t↕♦ r❛ ♠ët ❜↔♥❣ ❝❤ù❛ t✛ ❧➺ ✈è♥ ❝❤♦ t➜t ❝↔ ❝→❝ ♣❤➙♥ ❦❤ó❝✳ ❇↔♥❣ s❛✉ ✤â ❝â t❤➸ ✤÷đ❝ sû ❞ư♥❣ ✤➸ ❣→♥ t✛ ❧➺ ✈è♥ ❝❤♦ ♠ët ❝ì sð✱ ❞ü❛ tr➯♥ ♥❤ú♥❣ ✤➦❝ ✤✐➸♠ ✤â✳ ▼ët ❜↔♥❣ t✛ ❧➺ ố ữ tr ữợ ổ õ t [8] ỗ tr t ✈è♥ ✷✻ ❈❤÷ì♥❣ ✸✳ Ù◆● ❉Ư◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ✷✼ ❍➻♥❤ ✸✳✶✿ ❍➻♥❤ ♠✐♥❤ ❤å❛ t✛ ❧➺ ✈è♥ ❦✐♥❤ t ũ ỗ ởt số ữủ ♣❤➙♥ ✤♦↕♥✱ ♥❤÷♥❣ ❦❤ỉ♥❣ ♣❤↔✐ t➜t ❝↔ ❝→❝ ❦➳t ❤đ♣ õ t õ tr ữợ õ ❝â ✤÷đ❝ t✛ ❧➺ ✈è♥ ❝❤♦ ❝→❝ ✤✐➸♠ ♥➡♠ tr♦♥❣ ❣✐ỵ✐ ❤↕♥✱ ❝➛♥ ♣❤↔✐ ❝â ♣❤➨♣ ♥ë✐ s✉② ✤❛ ❝❤✐➲✉✳ ◆ë✐ s✉② t✉②➳♥ t➼♥❤ ✤❛ ❝❤✐➲✉ ✤÷đ❝ ①❡♠ ①➨t tr♦♥❣ ự ởt số ỵ ổ tự t➼♥❤ ✤ì♥ ❣✐↔♥✱ tè❝ ✤ë t➼♥❤ t♦→♥ ♥❤❛♥❤ ✈➔ ♥â ❤ú✉ ➼❝❤ ❝❤♦ ✈✐➺❝ ①➜♣ ①➾ ❝→❝ ❣✐→ trà ♥ë✐ s✉②✳ ✸✳✶ ❙û ❞ö♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ♠ët ❝❤✐➲✉ ✤➸ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ❚❛ ❝â ♠ët ❜↔♥❣ ❝❤ù❛ t✛ ❧➺ ❊❈ ❧➔ ♠ët ❤➔♠ ①→❝ s✉➜t ♠➦❝ ✤à♥❤ ✭P❉✮✱ ✈ỵ✐ t➜t ❝↔ ❝→❝ ②➳✉ tè rõ✐ r♦ ❦❤→❝ ✤÷đ❝ ❣✐ú ❝è ✤à♥❤✳ ❈❤÷ì♥❣ ✸✳ Ù◆● ❉Ư◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ✷✽ ❇↔♥❣ ✸✳✶✿ ❇↔♥❣ ❝❤ù❛ t✛ ❧➺ P❉(%) ✈➔ t✛ ❧➺ ❊❈(%) P❉✭%✮ ❚✛ ❧➺ ❊❈✭%✮ ✵✱✵✶✵ ✵✱✺✷ ✵✱✵✷✵ ✵✱✾✷ ✵✱✵✹✵ ✶✱✸✽ ✵✱✵✽✵ ✷✱✶✼ ✵✱✷✵✵ ✸✱✺✻ ✵✱✵✹✺ ✺✱✽✽ ✶✱✵✵✵ ✾✱✽✼ ✷✱✵✵✵ ✶✺✱✻✵ ✹✱✺✵✵ ✷✻✱✶✶ ✽✱✺✵✵ ✸✽✱✸✹ ✷✵✱✵✵✵ ✻✻✱✽✼ ❱ỵ✐ t✛ ❧➺ P❉ ð ♠ù❝ 6, 5% t❤➻ t✛ ❧➺ ❊❈ ❧➔ ❜❛♦ ♥❤✐➯✉ %❄ ❉ü❛ ✈➔♦ ❜↔♥❣ tr➯♥✱ ❝❤ó♥❣ t❛ ❝â t❤➸ ÷ỵ❝ t➼♥❤ t✛ ❧➺ ❊❈ ð ♠ù❝ ①→❝ s✉➜t ♠➦❝ ✤à♥❤ ❝õ❛ ♥â ❧➔ 6, 5% ❜➡♥❣ ❝→❝❤ sû ❞ö♥❣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤✳ ❍➻♥❤ ✸✳✷✿ ▼æ ♣❤ä♥❣ t✛ ❧➺ ❊❈ ❝➛♥ ♥ë✐ s✉② tr♦♥❣ ✤♦↕♥ ❆❇ ❈❤ó♥❣ t❛ ❝â t ữợ t t ự 6, 5% P❉ ❧➔ tr✉♥❣ ❜➻♥❤ ❝â trå♥❣ sè ❝õ❛ ❝→❝ ✤✐➸♠ ❧➙♥ ❝➟♥ ❤♦➦❝ ❝→❝ ✤♦↕♥ ✤÷í♥❣ ❝❤✉➞♥ ❤â❛ ❣✐ú❛ ❝→❝ B(x1 , y1 ) tr➯♥ ♠ët ✤♦↕♥ ✤÷í♥❣ tr♦♥❣ ❤➻♥❤ ✸✳✷✱ ❝❤ó♥❣ t❛ ❝â t❤➸ t➻♠ t❤➜② ✤✐➸♠ C(x, y)✳ ●✐↔ sû t✛ ❧➺ ❊❈ ❧➔ ❤➔♠ ①→❝ s✉➜t ♠➦❝ ✤à♥❤ ✭P❉✮ y = f (x)✳ ✣➸ ♥ë✐ s✉② ✤✐➸♠ C(x, y) t❛ →♣ ❞ư♥❣ ❝ỉ♥❣ t❤ù❝ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ ❣✐ú❛ ❤❛✐ ✤✐➸♠ A(x0 , y0 )✱ ✈➔ B(x1 , y1 ) ✤✐➸♠ ❆ ✈➔ ❇✳ ❈❤♦ ❝→❝ ✤✐➸♠ y= A(x0 , y0 )✱ ✈➔ x1 − x x − x0 y0 + y1 x1 − x0 x1 − x0 ❱ỵ✐ ① ❧➔ t❤❛♠ sè ❜✐➸✉ ❞✐➵♥ ①→❝ s✉➜t ♠➦❝ ✤à♥❤ ❝õ❛ ❦❤♦↔♥ ✈❛② y = f (x) ❧➔ t✛ ❧➺ ❊❈ ❜✐➸✉ ❞✐➵♥ ❤➔♠ ①→❝ s✉➜t ♠➦❝ ✤à♥❤ P❉ %✳ ❈❤÷ì♥❣ ✸✳ Ù◆● ❉Ư◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ✷✾ ❙û ❞ư♥❣ ♣❤➛♥ ♠➲♠ t➼♥❤ t♦→♥ ❘✱ ❝❤ó♥❣ t❛ ❝â t❤➸ t➼♥❤ t✛ ❧➺ ❊❈ ❝❤♦ ❦❤♦↔♥ ✈❛② ✤÷đ❝ ✤➲ ❝➟♣✳ ❱➟② ù♥❣ ✈ỵ✐ t✛ ❧➺ P❉ ð ♠ù❝ ✻✱✺% t❤➻ t✛ ❧➺ ❊❈ ❧➔ ✸✷✱✷✷✺%✳ ✸✳✷ ❙û ❞ö♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❤❛✐ ❝❤✐➲✉ ✤➸ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ❈❤ó♥❣ t❛ ❤➣② ①❡♠ ①➨t ♠ët ✈➼ ❞ö tr♦♥❣ ✤â t❛ ❝â ♠ët ❜↔♥❣ ❝❤ù❛ t✛ ❧➺ ❊❈ t❤❡♦ ❦ý ❤↕♥ ✈➔ t÷ì♥❣ q✉❛♥✳ ❇↔♥❣ ✸✳✷✿ ❇↔♥❣ ❝❤ù❛ ❦➻ ❤↕♥ ✭♥➠♠✮✱ t÷ì♥❣ q✉❛♥(%) ✈➔ t✛ ❧➺ ❊❈(%) ❑➻ ❤↕♥ ❚÷ì♥❣ q✉❛♥% ❚✛ ❧➺ ❊❈ % ✶✱✵ ✷✵% ✽✱✷✷% ✶✱✵ ✸✵% ✶✶✱✸✵% ✵✱✺ ✷✵% ✹✱✻✷% ✵✱✺ ✸✵% ✻✱✺✼% ❱ỵ✐ ❦➻ ❤↕♥ ❝❤♦ ✈❛② ✵✱✼ ♥➠♠ ✈➔ t÷ì♥❣ q✉❛♥ ✷✺% t❤➻ t✛ ❧➺ ❊❈ ❧➔ ❜❛♦ ♥❤✐➯✉ ♣❤➛♥ tr➠♠ ? ❚❛ ❝â t❤➸ t➼♥❤ t✛ ❧➺ ❊❈ t÷ì♥❣ ù♥❣ ❜➡♥❣ ❝→❝❤ sû ❞ư♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ✷ ❝❤✐➲✉✳ ❍➻♥❤ ✸✳✸ ữợ t ú t õ t ❞✉♥❣ ✈➜♥ ✤➲ ♥➔②✳ ❈❤÷ì♥❣ ✸✳ Ù◆● ❉Ư◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ✸✵ ❍➻♥❤ ✸✳✸✿ ❚✛ ❧➺ ❊❈ ❝➛♥ ♥ë✐ s✉② tr♦♥❣ ❤➻♥❤ ❝❤ú ♥❤➟t ❆❇❈❉ ●✐↔ sû t✛ ❧➺ ❊❈ ❜✐➸✉ ❞✐➵♥ t❤➔♥❤ ♠ët ❤➔♠ v = f (x, y) tr♦♥❣ ✤â ❜✐➳♥ ① ❜✐➸✉ ❞✐➵♥ t÷ì♥❣ q✉❛♥ ❣✐ú❛ ♥❤ú♥❣ ♥❣÷í✐ ✈❛② ❦❤→❝ ♥❤❛✉ tr♦♥❣ ❞❛♥❤ ♠ư❝ ✤➛✉ t÷ (%) ✈➔ ❜✐➳♥ ② ❜✐➸♥ ❞✐➵♥ t❤í✐ ❤↕♥ ❝á♥ ❧↕✐ ❝õ❛ ❦❤♦↔♥ ✈❛② ✭♥➠♠✮✳ ✣➦t ❜➔✐ t♦→♥ ✈➔♦ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❤❛✐ ❝❤✐➲✉✱ t❛ ❝â ❤➔♠ v = f (x, y) ố tữỡ ự ợ ố t ❊❈ ✤➣ ❜✐➳t t÷ì♥❣ q✉❛♥ ✈➔ ❦➻ ❤↕♥ ❦❤→❝ ♥❤❛✉ ❧➔ ❆✱ ❇✱ ❈✱ ❉ ♥❤÷ tr♦♥❣ ❤➻♥❤ ✸✳✸✳ ❍➻♥❤ ❝❤ú ♥❤➟t ❆❇❈❉ ✤÷đ❝ ❝❤✐❛ t❤➔♥❤ ❜è♥ ✈ò♥❣ t❤❡♦ ❝→❝ ❞á♥❣ ① ✈➔ ②✳ ❑❤✐ ✤â✱ ✤➸ ♥ë✐ s✉② ✤✐➸♠ ❊ t❛ →♣ ❞ư♥❣ ❝ỉ♥❣ t❤ù❝ ♥ë✐ s✉② tr♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ❤❛✐ ❝❤✐➲✉✳ ❑❤✐ ✤â Va = (x1 − x) (y − y0 ) (x − x0 ) (y − y0 ) ; Vb = (x1 − x0 ) (y1 − y0 ) (x1 − x0 ) (y1 − y0 ) Vc = (x1 − x) (y1 − y) (x − x0 ) (y1 − y) ; Vd = (x1 − x0 ) (y1 − y0 ) (x1 − x0 ) (y1 − y0 ) v = f (x, y) ✤÷đ❝ t➼♥❤ t❤❡♦ ❝ỉ♥❣ t❤ù❝✿ V = Va A + Vb B + Vc C + Vd D ❙û ❞ö♥❣ ♣❤➛♥ ♠➲♠ t➼♥❤ t♦→♥ ❘✱ ❝❤ó♥❣ t❛ ❝â t❤➸ t➼♥❤ t✛ ❧➺ ❊❈ ❝❤♦ ❦❤♦↔♥ ✈❛② ✤÷đ❝ ✤➲ ❝➟♣✳ ❈❤÷ì♥❣ ✸✳ Ù◆● ❉Ö◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ✸✶ ❱➟② ù♥❣ ợ tữỡ q % t t✛ ❧➺ ❊❈ ❧➔ ✼✱✷✻% ✸✳✸ ❙û ❞ö♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❜❛ ❝❤✐➲✉ ✤➸ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ◆❤÷ ✤➣ ✤➲ ❝➟♣ ð tr ởt ữợ t õ t❤➸ ❝❤ù❛ ❤➔♥❣ tr➠♠ ♥❣❤➻♥ t✛ ❣✐→✳ ✣➸ ❞➵ ♠✐♥❤ ❤å❛ tr♦♥❣ ✈➼ ❞ư s❛✉✱ ❝❤ó♥❣ tỉ✐ ❝♦✐ P❉ ❧➔ ♠ët ❜✐➳♥ ❝è ✤à♥❤ ✈➔ ❞♦ ✤â ❝❤➾ ♥ë✐ s✉② q✉❛ ❜❛ ❜✐➳♥ ❧✐➯♥ tư❝ ❝á♥ ❧↕✐✿ ❚÷ì♥❣ q✉❛♥✱ ▲●❉ ✈➔ ❦➻ ❤↕♥✳ ❚r♦♥❣ ✈➼ ❞ư ♥➔②✱ ❝❤ó♥❣ tỉ✐ ✤÷đ❝ ❝❤♦ ✈❛② ✈ỵ✐ ❝→❝ ✤➦❝ ✤✐➸♠ s❛✉✿ ❦➻ ❤↕♥ ✵✱✼ ✭♥➠♠✮✱ ❚÷ì♥❣ q✉❛♥ ✷✺% ✈➔ ▲●❉ ✷✵% ✈➔ ♠✉è♥ t➻♠ t✛ ❧➺ ❊❈ ♥ë✐ s✉②✳ ❇↔♥❣ ✸✳✸✿ ❇↔♥❣ ❝❤ù❛ ❦➻ ❤↕♥ ✭♥➠♠✮✱ t÷ì♥❣ q✉❛♥ (%)✱ ▲●❉ (%) ✈➔ t✛ ❧➺ ❊❈ (%) ❑➻ ❤↕♥ ❚÷ì♥❣ q✉❛♥ (%) ▲●❉ (%) ❚✛ ❧➺ ❊❈ (%) ✵✱✺ ✷✵% ✶✺% ✸✱✵✽% ✵✱✺ ✷✵% ✷✺% ✹✱✻✷% ✵✱✺ ✸✵% ✶✺% ✹✱✹✼% ✵✱✺ ✸✵% ✷✺% ✻✱✺✼% ✶✱✵ ✷✵% ✶✺% ✺✱✻✷% ✶✱✵ ✷✵% ✷✺% ✽✱✷✷% ✶✱✵ ✸✵% ✶✺% ✼✱✽✺% ✶✱✵ ✸✵% ✷✺% ✶✶✱✸✵% ❱ỵ✐ ❦➻ ❤↕♥ ❧➔ ✵✱✼ ✭♥➠♠✮✱ t÷ì♥❣ q✉❛♥ ❧➔ ✷✺(%)✱ ▲●❉ ❧➔ ✷✵(%) t❤➻ t✛ ❧➺ ❊❈ t÷ì♥❣ ù♥❣ ❧➔ ❜❛♦ ♥❤✐➯✉ ♣❤➛♥ tr➠♠❄ ❈❤÷ì♥❣ ✸✳ Ù◆● ❉Ö◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ ✸✷ ❚❛ ❝â t❤➸ t➼♥❤ t✛ ❧➺ ❊❈ t÷ì♥❣ ù♥❣ ❜➡♥❣ ❝→❝❤ sû ❞ư♥❣ ♣❤➨♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✸ ữợ t ú t ❝â t❤➸ ❤➻♥❤ ❞✉♥❣ ✈➜♥ ✤➲ ♥➔②✳ ❍➻♥❤ ✸✳✹✿ ▼æ ♣❤ä♥❣ t✛ ❧➺ ❊❈ ❝➛♥ ♥ë✐ s✉② tr♦♥❣ ❧➠♥❣ trö ❆❇❈❉❊❋●❍ ●✐↔ sû t✛ ❧➺ ❊❈ ❜✐➸✉ ❞✐➵♥ ♠ët ❤➔♠ p = f (x, y, z) tr♦♥❣ ✤â ❜✐➳♥ ① ❜✐➸✉ ❞✐➵♥ ❦➻ ❤↕♥ ❝á♥ ❧↕✐ ❝õ❛ ❦❤♦↔♥ ✈❛② ✭♥➠♠✮✱ ❜✐➳♥ ② ❜✐➸✉ ❞✐➵♥ t÷ì♥❣ q✉❛♥ ❣✐ú❛ ♥❤ú♥❣ ♥❣÷í✐ ✈❛② ❦❤→❝ ♥❤❛✉ tr♦♥❣ ❞❛♥❤ ♠ư❝ ✤➛✉ t÷ ❞✐➵♥ t✛ ❧➺ ▲●❉ (%) ✈➔ ❜✐➳♥ ③ ❜✐➸✉ (%)✳ ✣➦t ❜➔✐ t♦→♥ ✈➔♦ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❜❛ ❝❤✐➲✉✱ t❛ ❝â ❤➔♠ p = f (x, y, z) ✈➔ ✽ ✤✐➸♠ t÷ì♥❣ ù♥❣ ✈ỵ✐ t→♠ t✛ ❧➺ ❊❈ ✤➣ ❜✐➳t ❧➔ ❆✱ ❇✱ ❈✱ ❉✱ ❊✱ ❋✱ ●✱ ❍ ♥❤÷ tr♦♥❣ ❤➻♥❤ ✸✳✹✳ ❆❇❈❉❊❋●❍ ❧➔ ❧➠♥❣ trö ♣❤➙♥ ❤♦↕❝❤ ✈➔♦ t→♠ ❦❤è✐ ❜ð✐ ❝→❝ ♠➦t ♣❤➥♥❣ ①✱ ② ✈➔ ③✳ ❑❤✐ ✤â ✤➸ ♥ë✐ s✉② ✤✐➸♠ P t❛ →♣ ❞ư♥❣ ❝ỉ♥❣ t❤ù❝ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ❜❛ ❝❤✐➲✉✳ Na = (x1 − x)(y1 − y)(z − z0 ) (x1 − x)(y − y0 )(z − z0 ) ; Nb = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) ❈❤÷ì♥❣ ✸✳ Ù◆● ❉Ư◆● ❈Õ❆ ❇❷◆● ❚➐▼ ❑■➌▼ Nc = (x − x0 )(y1 − y)(z − z0 ) (x − x0 )(y − y0 )(z − z0 ) ; Nd = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) Ne = (x1 − x)(y − y0 )(z1 − z) (x1 − x)(y1 − y)(z1 − z) ; Nf = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) Ng = (x − x0 )(y1 − y)(z1 − z) (x − x0 )(y − y0 )(z1 − z) ; Nh = (x1 − x0 )(y1 − y0 )(z1 − z0 ) (x1 − x0 )(y1 − y0 )(z1 − z0 ) ✸✸ p = f (x, y, z) ✤÷đ❝ t➼♥❤ t❤❡♦ ❝ỉ♥❣ t❤ù❝✿ p = Na A + Nb B + Nc C + Nd D + Ne E + Nf F + Ng G + Nh H ❑❤✐ ✤â ❙û ❞ö♥❣ ♣❤➛♥ ♠➲♠ t➼♥❤ t♦→♥ ❘✱ ❝❤ó♥❣ t❛ ❝â t❤➸ t➼♥❤ t✛ ❧➺ ❊❈ ❝❤♦ ❦❤♦↔♥ ữủ ự ợ ợ tớ tữỡ q % ▲●❉ ✷✵% t❤➻ t✛ ❧➺ ❊❈ ❧➔ ✻✱✶✶%✳ ❑➳t ❧✉➟♥ ◗✉❛ q✉→ tr➻♥❤ ❧➔♠ ❦❤â❛ ❧✉➟♥✱ s❛✉ ❦❤✐ ♣❤➙♥ t➼❝❤✱ t➻♠ ❤✐➸✉ ❝❤✉♥❣ ✈➲ ❜↔♥❣ t➻♠ ❦✐➳♠✱ ✈➲ ♣❤÷ì♥❣ ♣❤→♣ ♥ë✐ s✉②✱ tæ✐ ✤➣ ❜ê s✉♥❣ ❝❤♦ ♠➻♥❤ ♥❤✐➲✉ ❦✐➳♥ tự qỵ ổ t s ỡ ✤õ ❤ì♥ ✈➲ ♣❤÷ì♥❣ ♣❤→♣ ♥ë✐ s✉② t✉②➳♥ t➼♥❤ ✤÷đ❝ sû ❞ư♥❣ tr♦♥❣ ❜↔♥❣ t➻♠ ❦✐➳♠✳ ❚ỉ✐ ✤➣ ❝â t❤➯♠ ỳ tự ợ t ữủ tr ♠ët ❤➔♠ ❦❤✐ t❛ ❦❤æ♥❣ ❜✐➳t ❝❤➼♥❤ ①→❝ ❤➔♠ ✤â ♥❤÷ t❤➳ ♥➔♦ ♠➔ ❝❤➾ t❤ỉ♥❣ q✉❛ ❝→❝ ✤✐➸♠ ❞ú ❧✐➺✉ t❤✉ë❝ ❤➔♠ ✤â✳ ❱➔ tø ✤â✱ ❝â t❤➸ →♣ ❞ö♥❣ ✈➔♦ ❜➔✐ t♦→♥ t➻♠ t✛ ❧➺ ✈è♥ ❦✐♥❤ t➳ ❦❤✐ ✤➣ ❜✐➳t ♠ët ❜↔♥❣ ❝❤ù❛ ❝→❝ t✛ ❧➺ ①→❝ ✤à♥❤ ✈è♥ ❦✐♥❤ t➳✳ ❚✉② ♥❤✐➯♥ ❞♦ t❤í✐ ❣✐❛♥ ❝â ❤↕♥ ✈➔ ❝❤÷❛ ❝â ♥❤✐➲✉ ❦✐♥❤ ♥❣❤✐➺♠ tr♦♥❣ ❝ỉ♥❣ t→❝ ♥❣❤✐➯♥ ❝ù✉ ❦❤♦❛ ❤å❝ ♥➯♥ ♥❤ú♥❣ ✈➜♥ ✤➲ ♠➔ tæ✐ tr➻♥❤ ❜➔② tr♦♥❣ ❦❤â❛ ❧✉➟♥ ♥➔② s➩ ❦❤æ♥❣ tr→♥❤ ❦❤ä✐ ♥❤ú♥❣ t❤✐➳✉ sât✳ ❱➻ ✈➟② tè✐ r➜t ♠♦♥❣ sü t❤æ♥❣ t ổ ữủ ỵ õ õ qỵ t ổ ❦❤â❛ ❧✉➟♥ ❝õ❛ tỉ✐ ✤÷đ❝ ❤♦➔♥ t❤✐➺♥ ❤ì♥✳ ✸✹ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ❬✶❪ ❍❡♥r② ❘✳ ❑❛♥❣✱ ❚❤r❡❡✲❉✐♠❡♥s✐♦♥❛❧ ▲♦♦❦✉♣ ❚❛❜❧❡ ✇✐t❤ ■♥t❡r♣♦❧❛t✐♦♥✱ ❈❤❛♣t❡r ✾✱ ❈♦♠♣✉t❛t✐♦♥❛❧ ❈♦❧♦r ❚❡❝❤♥♦❧♦❣②✱ ✷✵✵✻ ❬✷❪ ❘✐❝❦ ❲❛❣♥❡r✱ ▼✉❧t✐✲▲✐♥❡❛r ■♥t❡r♣♦❧❛t✐♦♥ ❬✸❪ ❈❤r✐s ❲✐❧❝♦①✱ ❆ ♠❡t❤♦❞♦❧♦❣② ❢♦r ❛✉t♦♠❛t❡❞ ❧♦♦❦✉♣ t❛❜❧❡ ♦♣t✐♠✐③❛✲ t✐♦♥ ♦❢ s❝✐❡♥t✐❢✐❝ ❛♣♣❧✐❝❛t✐♦♥s ❬✹❪ ❤tt♣s✿//❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣/✇✐❦✐/▲♦♦❦✉♣❴t❛❜❧❡ ❬✺❪ ❤tt♣s✿//❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣/✇✐❦✐/▲✐♥❡❛r❴✐♥t❡r♣♦❧❛t✐♦♥ ❬✻❪ ❤tt♣s✿//❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣/✇✐❦✐/❇✐❧✐♥❡❛r❴✐♥t❡r♣♦❧❛t✐♦♥ ❬✼❪ ❤tt♣s✿//❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣/✇✐❦✐/❚r✐❧✐♥❡❛r❴✐♥t❡r♣♦❧❛t✐♦♥ ❬✽❪ ❤tt♣s✿//❛♥❛❧②t✐❝sr✉s❡rs✳❜❧♦❣✴✉s✐♥❣❴♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧❴❧✐♥❡❛r❴✐♥t❡r♣♦❧❛t✐♦♥ ❴t♦❴❢✐♥❞❴❡❝♦♥♦♠✐❝❴❝❛♣✐t❛❧❴r❛t❡s ✸✺
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