❚r÷í♥❣ ✣❍ ❚➔✐ ❝❤➼♥❤✲▼❛r❦❡t✐♥❣ ❑❤♦❛ ❈ì ❇↔♥ ❈ë♥❣ ❤á❛ ❳➣ ❤ë✐ ❈❤õ ♥❣❤➽❛ ❱✐➺t ◆❛♠ ✣ë❝ ❧➟♣✲❚ü ❞♦✲❍↕♥❤ ♣❤ó❝ ✣➋ ❚❍■ ❙➮ ✶ ▼➷◆ ❚❖⑩◆ ❈❆❖ ❈❻P ✭❈▲❈✮ ❚❤í✐ ❣✐❛♥✿ ✼✺ ♣❤ót ✭❦❤ỉ♥❣ ❦➸ ❝❤➨♣✴♣❤→t ✤➲✮ ✶✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ ❣✐ỵ✐ ❤↕♥ lim (cos(x)) x2 x→0 ✷✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ t➼❝❤ ♣❤➙♥ s✉② rë♥❣ +∞ √ dx x x2 − ✸✳ ✭✶✱✺ ✤✐➸♠✮ ❙û ❞ö♥❣ ✈✐ ♣❤➙♥ t♦➔♥ ♣❤➛♥ ✤➸ t➼♥❤ ❣➛♥ ✤ó♥❣ ❣✐→ trà ❜✐➸✉ t❤ù❝ s❛✉ (2, 99)2 + (4, 02)2 A= ✹✳ ✭✷✱✵ ✤✐➸♠✮ ❚➻♠ ❝ü❝ trà ❝õ❛ ❤➔♠ ❤❛✐ ❜✐➳♥ s❛✉ f (x, y) = 2x2 + y − 4x + ✺✳ ✭✷✱✵ ✤✐➸♠✮ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ✶ s❛✉ y − 2xy = x3 ✻✳ ✭✶✱✺ ✤✐➸♠✮ ❈❤♦ ❤➔♠ sè f (x) =   1 1+e x−2 , ✈ỵ✐ x = , ✈ỵ✐ x = 0 ❍➔♠ sè ❢✭①✮ ❝â ❧✐➯♥ tử t ổ ú ỵ ❦❤ỉ♥❣ ✤÷đ❝ t❤❛♠ ❦❤↔♦ t➔✐ ❧✐➺✉✳ ✷✳ ❈→♥ ❜ë ❝♦✐ t❤✐ ❦❤æ♥❣ ❣✐↔✐ t❤➼❝❤ ❣➻ t❤➯♠✳ ❇ë ♠æ♥ ❚♦→♥✲❚❤è♥❣ ❦➯ ✭❞✉②➺t✮ ◆❣÷í✐ r❛ ✤➲ ✶ ❚r÷í♥❣ ✣❍ ❚➔✐ ❝❤➼♥❤✲▼❛r❦❡t✐♥❣ ❑❤♦❛ ❈ì ❇↔♥ ❈ë♥❣ ❤á❛ ❳➣ ❤ë✐ ❈❤õ ♥❣❤➽❛ ❱✐➺t ◆❛♠ ✣ë❝ ❧➟♣✲❚ü ❞♦✲❍↕♥❤ ♣❤ó❝ ✣➋ ❚❍■ ❙➮ ✷ ▼➷◆ ❚❖⑩◆ ❈❆❖ ❈❻P ✭❈▲❈✮ ❚❤í✐ ❣✐❛♥✿ ✼✺ ♣❤ót ✭❦❤ỉ♥❣ ❦➸ ❝❤➨♣✴♣❤→t ✤➲✮ ✶✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ ❣✐ỵ✐ ❤↕♥ x+2 x−3 lim x→±∞ 3x+4 ✷✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ t➼❝❤ ♣❤➙♥ s✉② rë♥❣ +∞ e−x sin(x)dx ✸✳ ✭✶✱✺ ✤✐➸♠✮ ❙û ❞ö♥❣ ✈✐ ♣❤➙♥ t♦➔♥ ♣❤➛♥ ✤➸ t➼♥❤ ❣➛♥ ✤ó♥❣ ❣✐→ trà ❜✐➸✉ t❤ù❝ s❛✉ A= (1, 99)2 + (3, 02)2 ✹✳ ✭✷✱✵ ✤✐➸♠✮ ❚➻♠ ❝ü❝ trà ❝õ❛ ❤➔♠ ❤❛✐ ❜✐➳♥ s❛✉ f (x, y) = 4x + 2y − x2 − y ✺✳ ✭✷✱✵ ✤✐➸♠✮ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ✶ s❛✉ y + 4y = x2 e−4x ✻✳ ✭✶✱✺ ✤✐➸♠✮ ❈❤♦ ❤➔♠ sè f (x) = sin3 (x) x , ✈ỵ✐ x = a , ✈ỵ✐ x = ❳→❝ ✤à♥❤ ❛ ✤➸ ❤➔♠ sè ❢✭①✮ tử t ú ỵ ổ ✤÷đ❝ t❤❛♠ ❦❤↔♦ t➔✐ ❧✐➺✉✳ ✷✳ ❈→♥ ❜ë ❝♦✐ t❤✐ ❦❤æ♥❣ ❣✐↔✐ t❤➼❝❤ ❣➻ t❤➯♠✳ ❇ë ♠æ♥ ❚♦→♥✲❚❤è♥❣ ❦➯ ✭❞✉②➺t✮ ◆❣÷í✐ r❛ ✤➲ ✷ ❚r÷í♥❣ ✣❍ ❚➔✐ ❝❤➼♥❤✲▼❛r❦❡t✐♥❣ ❑❤♦❛ ❈ì ❇↔♥ ❈ë♥❣ ❤á❛ ❳➣ ❤ë✐ ❈❤õ ♥❣❤➽❛ ❱✐➺t ◆❛♠ ✣ë❝ ❧➟♣✲❚ü ❞♦✲❍↕♥❤ ♣❤ó❝ ✣➋ ❚❍■ ❙➮ ✸ ▼➷◆ ❚❖⑩◆ ❈❆❖ ❈❻P ✭❈▲❈✮ ❚❤í✐ ❣✐❛♥✿ ✼✺ ♣❤ót ✭❦❤ỉ♥❣ ❦➸ ❝❤➨♣✴♣❤→t ✤➲✮ ✶✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ ❣✐ỵ✐ ❤↕♥ sin(x) x−sin(x) sin(x) x lim x→0 ✷✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ t➼❝❤ ♣❤➙♥ s✉② rë♥❣ +∞ e−x cos(x)dx ✸✳ ✭✶✱✺ ✤✐➸♠✮ ❙û ❞ö♥❣ ✈✐ ♣❤➙♥ t♦➔♥ ♣❤➛♥ ✤➸ t➼♥❤ ❣➛♥ ✤ó♥❣ ❣✐→ trà ❜✐➸✉ t❤ù❝ s❛✉ (3, 99)2 + (5, 02)2 A= ✹✳ ✭✷✱✵ ✤✐➸♠✮ ❚➻♠ ❝ü❝ trà ❝õ❛ ❤➔♠ ❤❛✐ ❜✐➳♥ s❛✉ f (x, y) = (x + y − 9)(4x + 3y) − 6xy ✺✳ ✭✷✱✵ ✤✐➸♠✮ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ✶ s❛✉ xy + 2y = x−3 ✻✳ ✭✶✱✺ ✤✐➸♠✮ ❈❤♦ ❤➔♠ sè f (x) =   1 x+2 x−3 , ✈ỵ✐ x = , ✈ỵ✐ x = a ❳→❝ ✤à♥❤ ❛ ✤➸ số tử t ú ỵ ❙✐♥❤ ✈✐➯♥ ❦❤ỉ♥❣ ✤÷đ❝ t❤❛♠ ❦❤↔♦ t➔✐ ❧✐➺✉✳ ✷✳ ❈→♥ ❜ë ❝♦✐ t❤✐ ❦❤æ♥❣ ❣✐↔✐ t❤➼❝❤ ❣➻ t❤➯♠✳ ❇ë ♠æ♥ ❚♦→♥✲❚❤è♥❣ ❦➯ ✭❞✉②➺t✮ ◆❣÷í✐ r❛ ✤➲ ✸ ❚r÷í♥❣ ✣❍ ❚➔✐ ❝❤➼♥❤✲▼❛r❦❡t✐♥❣ ❑❤♦❛ ❈ì ❇↔♥ ❈ë♥❣ ❤á❛ ❳➣ ❤ë✐ ❈❤õ ♥❣❤➽❛ ❱✐➺t ◆❛♠ ✣ë❝ ❧➟♣✲❚ü ❞♦✲❍↕♥❤ ♣❤ó❝ ✣➋ ❚❍■ ❙➮ ✹ ▼➷◆ ❚❖⑩◆ ❈❆❖ ❈❻P ✭❈▲❈✮ ❚❤í✐ ❣✐❛♥✿ ✼✺ ♣❤ót ✭❦❤ỉ♥❣ ❦➸ ❝❤➨♣✴♣❤→t ✤➲✮ ✶✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ ❣✐ỵ✐ ❤↕♥ lim x→0 ln cos(x) x2 ✷✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ t➼❝❤ ♣❤➙♥ s✉② rë♥❣ +∞ x3 e−x dx ✸✳ ✭✶✱✺ ✤✐➸♠✮ ❙û ❞ö♥❣ ✈✐ ♣❤➙♥ t♦➔♥ ♣❤➛♥ ✤➸ t➼♥❤ ❣➛♥ ✤ó♥❣ ❣✐→ trà ❜✐➸✉ t❤ù❝ s❛✉ A = ln (2, 01)2 + (3, 99)2 ✹✳ ✭✷✱✵ ✤✐➸♠✮ ❚➻♠ ❝ü❝ trà ❝õ❛ ❤➔♠ ❤❛✐ ❜✐➳♥ f (x, y) = 2x2 −6y , ✈ỵ✐ r➔♥❣ ❜✉ë❝ x+2y = ✺✳ ✭✷✱✵ ✤✐➸♠✮ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ s❛✉ y ” − 6y + 9y = 2x2 − x + ✻✳ ✭✶✱✺ ✤✐➸♠✮ ❈❤♦ ❤➔♠ sè f (x) =   1 x+2 x−1 , ✈ỵ✐ x = , ✈ỵ✐ x = 0 ❍➔♠ sè ❢✭①✮ ❝â ❧✐➯♥ tư❝ ✈ỵ✐ ♠å✐ x ∈ (−∞, +∞) ❤❛② ❦❤ỉ♥❣❄✳ ❈❤ó þ✿ ✶✳ ❙✐♥❤ ✈✐➯♥ ❦❤ỉ♥❣ ✤÷đ❝ t❤❛♠ ❦❤↔♦ t➔✐ ❧✐➺✉✳ ✷✳ ❈→♥ ❜ë ❝♦✐ t❤✐ ❦❤æ♥❣ ❣✐↔✐ t❤➼❝❤ ❣➻ t❤➯♠✳ ❇ë ♠ỉ♥ ❚♦→♥✲❚❤è♥❣ ❦➯ ✭❞✉②➺t✮ ◆❣÷í✐ r❛ ✤➲ ✹ ❚r÷í♥❣ ✣❍ ❚➔✐ ❝❤➼♥❤✲▼❛r❦❡t✐♥❣ ❑❤♦❛ ❈ì ❇↔♥ ❈ë♥❣ ❤á❛ ❳➣ ❤ë✐ ❈❤õ ♥❣❤➽❛ ❱✐➺t ◆❛♠ ✣ë❝ ❧➟♣✲❚ü ❞♦✲❍↕♥❤ ♣❤ó❝ ✣➋ ❚❍■ ❙➮ ✺ ▼➷◆ ❚❖⑩◆ ❈❆❖ ❈❻P ✭❈▲❈✮ ❚❤í✐ ❣✐❛♥✿ ✼✺ ♣❤ót ✭❦❤ỉ♥❣ ❦➸ ❝❤➨♣✴♣❤→t ✤➲✮ ✶✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ ❣✐ỵ✐ ❤↕♥ 1− lim x→0 cos(x) x2 ✷✳ ✭✶✱✺ ✤✐➸♠✮ ❚➼♥❤ t➼❝❤ ♣❤➙♥ s✉② rë♥❣ +∞ e−x dx + ex ✸✳ ✭✶✱✺ ✤✐➸♠✮ ❙û ❞ö♥❣ ✈✐ ♣❤➙♥ t♦➔♥ ♣❤➛♥ ✤➸ t➼♥❤ ❣➛♥ ✤ó♥❣ ❣✐→ trà ❜✐➸✉ t❤ù❝ s❛✉ A = ln (3, 01)2 + (4, 99)2 ✹✳ ✭✷✱✵ ✤✐➸♠✮ ❚➻♠ ❝ü❝ trà ❝õ❛ ❤➔♠ ❤❛✐ ❜✐➳♥ f (x, y) = x2 + 3xy − 5y , ✈ỵ✐ r➔♥❣ ❜✉ë❝ 2x + 3y = ✺✳ ✭✷✱✵ ✤✐➸♠✮ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ s❛✉ y ” − 9y + 20y = x2 e4x ✻✳ ✭✶✱✺ ✤✐➸♠✮ ❈❤♦ ❤➔♠ sè f (x) =   1 x+3 x−2 , ✈ỵ✐ x = , ✈ỵ✐ x = 0 ❍➔♠ sè ❢✭①✮ ❝â ❧✐➯♥ tư❝ ✈ỵ✐ ♠å✐ x ∈ (, +) ổ ú ỵ ổ ✤÷đ❝ t❤❛♠ ❦❤↔♦ t➔✐ ❧✐➺✉✳ ✷✳ ❈→♥ ❜ë ❝♦✐ t❤✐ ❦❤æ♥❣ ❣✐↔✐ t❤➼❝❤ ❣➻ t❤➯♠✳ ❇ë ♠æ♥ ❚♦→♥✲❚❤è♥❣ ❦➯ ✭❞✉②➺t✮ ◆❣÷í✐ r❛ ✤➲ ✺