ǵȜȦȖȠ ǿdzǾȀǶȂǥǸǮȄǥǷǻǮǾǼǯǼȀǮ ǵǺǮȀdzǺǮȀǶǸǶ ȅȎȟȐȖȘȜțȎțțȭ²ȣȐȖșȖț ǾȜȏȜȠȎȟȘșȎȒȎȱȠȪȟȭȕȕȎȐȒȎțȪȞȳȕțȖȣȢȜȞȚǰȳȒȝȜȐȳȒȳȒȜȕȎȐȒȎțȪ²ǰȖȚȎȱȠȓ ȝȜȕțȎȥȖȠȖ Ȑ ȏșȎțȘȡ Ǯ ǾȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ² ǰȖ ȚȎȱȠȓ ȕȎȝȖȟȎȠȖ ȐȏșȎțȘȎȣǯȠȎǰ. ǾȓȕȡșȪȠȎȠȐȖȘȜțȎțțȭȐȟȳȣȕȎȐȒȎțȪȏȡȒȓȐȖȘȜȞȖȟȠȎțȜȝȳȒȥȎȟȝȞȖȗȜȚȡȒȜ ȕȎȘșȎȒȳȐȐȖȧȜȴȜȟȐȳȠȖ ǾȓȕȡșȪȠȎȠ ȐȖȘȜțȎțțȭ ȕȎȐȒȎțȪ 1–26, 30 ȳ 31 ȏȡȒȓ ȕȎȞȎȣȜȐȎțȜ ȭȘ ȞȓȕȡșȪȠȎȠ ȒȓȞȔȎȐțȜȴȝȳȒȟȡȚȘȜȐȜȴȎȠȓȟȠȎȤȳȴȒșȭȐȖȝȡȟȘțȖȘȳȐȭȘȳȐȖȐȥȎșȖȚȎȠȓȚȎ ȠȖȘȡțȎȞȳȐțȳȟȠȎțȒȎȞȠȡ ǾȓȕȡșȪȠȎȠȐȖȘȜțȎțțȭȐȟȳȣȕȎȐȒȎțȪȏȡȒȓȕȎȞȎȣȜȐȎțȜȭȘȞȓȕȡșȪȠȎȠȒȓȞȔȎȐ țȜȴ ȝȳȒȟȡȚȘȜȐȜȴ ȎȠȓȟȠȎȤȳȴ Ȓșȭ ȐȖȝȡȟȘțȖȘȳȐ ȭȘȳ ȐȖȐȥȎșȖ ȚȎȠȓȚȎȠȖȘȡ țȎ ȝȞȜȢȳșȪțȜȚȡȞȳȐțȳ 1. 2. 3. 4. 5. ǥțȟȠȞȡȘȤȳȭȧȜȒȜȞȜȏȜȠȖȐȕȜȦȖȠȳ ǽȞȎȐȖșȎȐȖȘȜțȎțțȭȕȎȐȒȎțȪȕȎȕțȎȥȓțȜȝȓȞȓȒȘȜȔțȜȬțȜȐȜȬȢȜȞȚȜȬȕȎȐȒȎțȪ ǾȖȟȡțȘȖ ȒȜ ȕȎȐȒȎțȪ ȐȖȘȜțȎțȜ ȟȣȓȚȎȠȖȥțȜ ȏȓȕ ȟȠȞȜȑȜȑȜ ȒȜȠȞȖȚȎțțȭ ȝȞȜȝȜȞȤȳȗ ǰȳȒȝȜȐȳȒȎȗȠȓ șȖȦȓ ȝȳȟșȭ ȠȜȑȜ ȭȘ ǰȖ ȡȐȎȔțȜ ȝȞȜȥȖȠȎșȖ ȗ ȕȞȜȕȡȚȳșȖ ȕȎȐȒȎțțȭǰȖȘȜȞȖȟȠȜȐȡȗȠȓȭȘȥȓȞțȓȠȘȡȐȳșȪțȳȐȳȒȠȓȘȟȠȡȚȳȟȤȭȐȕȜȦȖȠȳ ǻȎȚȎȑȎȗȠȓȟȭȐȖȘȜțȎȠȖȐȟȳȕȎȐȒȎțțȭ ǰȖ ȚȜȔȓȠȓ ȟȘȜȞȖȟȠȎȠȖȟȭ ȒȜȐȳȒȘȜȐȖȚȖ ȚȎȠȓȞȳȎșȎȚȖ țȎȐȓȒȓțȖȚȖ țȎ ȟȠȜȞȳțȘȎȣDzșȭȕȞȡȥțȜȟȠȳǰȖȚȜȔȓȠȓȴȣȐȳȒȜȘȞȓȚȖȠȖȐȳȒȳȞȐȎȐȦȖ ǥțȟȠȞȡȘȤȳȭȧȜȒȜȕȎȝȜȐțȓțțȭȏșȎțȘȳȐȐȳȒȝȜȐȳȒȓȗǮǯȠȎǰ 1. ȁȏșȎțȘǮȕȎȝȖȟȡȗȠȓȥȳȠȘȜȕȑȳȒțȜȕȐȖȚȜȑȎȚȖȳțȟȠȞȡȘȤȳȴȒȜȘȜȔțȜȴȢȜȞȚȖ ȕȎȐȒȎțȪșȖȦȓȝȞȎȐȖșȪțȳțȎǰȎȦȡȒȡȚȘȡȐȳȒȝȜȐȳȒȳ 2. ǻȓȝȞȎȐȖșȪțȜ ȝȜȕțȎȥȓțȳ ȝȳȒȥȖȧȓțȳ ȐȳȒȝȜȐȳȒȳ Ȑ ȏșȎțȘȡ Ǯ ȏȡȒȓ ȕȎȞȎȣȜ ȐȎțȜȭȘȝȜȚȖșȘȜȐȳ ȍȘȧȜ ǰȖ ȝȜȕțȎȥȖșȖ ȐȳȒȝȜȐȳȒȪ ȒȜ ȭȘȜȑȜȟȪ ȳȕ ȕȎȐȒȎțȪ ² ȡ ȏșȎțȘȡ Ǯ țȓȝȞȎȐȖșȪțȜȠȜȚȜȔȓȠȓȐȖȝȞȎȐȖȠȖȴȴȕȎȚȎșȬȐȎȐȦȖȝȜȝȓȞȓȒțȬȝȜȕțȎȥȘȡ ȗȝȜȟȠȎȐȖȐȦȖțȜȐȡȭȘȝȜȘȎȕȎțȜțȎȕȞȎȕȘȎȣ 4. 5. 6. ȍȘȧȜ ǰȖ ȕȎȝȖȟȎșȖ ȐȳȒȝȜȐȳȒȪ ȒȜ ȭȘȜȑȜȟȪ ȳȕ ȕȎȐȒȎțȪ ² țȓȝȞȎȐȖșȪțȜ ȠȜȚȜȔȓȠȓȐȖȝȞȎȐȖȠȖȴȴȕȎȝȖȟȎȐȦȖțȜȐȖȗȐȎȞȳȎțȠȐȳȒȝȜȐȳȒȳȐȟȝȓȤȳȎșȪțȜ ȐȳȒȐȓȒȓțȖȣȚȳȟȤȭȣȏșȎțȘȎǮ ǰȖȘȜțȎȐȦȖ ȕȎȐȒȎțțȭ ȳ ² Ȑ ȕȜȦȖȠȳ ȎȘȡȞȎȠțȜ ȕȎȝȖȦȳȠȪ ȴȣțȳȞȜȕȐ·ȭȕȎțțȭȐȏșȎțȘȎȣǯȠȎǰ ǰȎȦ ȞȓȕȡșȪȠȎȠ ȕȎșȓȔȎȠȖȚȓ ȐȳȒ ȕȎȑȎșȪțȜȴ ȘȳșȪȘȜȟȠȳ ȝȞȎȐȖșȪțȖȣ ȐȳȒȝȜȐȳȒȓȗ ȕȎȝȖȟȎțȖȣ ȡ ȏșȎțȘȡ Ǯ ȳ ȝȞȎȐȖșȪțȜȑȜ ȞȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ²ȐȏșȎțȘȎȣǯȠȎǰ ǼȕțȎȗȜȚȖȐȦȖȟȪ ȳȕ ȳțȟȠȞȡȘȤȳȭȚȖ ȝȓȞȓȐȳȞȠȓ ȭȘȳȟȠȪ ȒȞȡȘȡ ȕȜȦȖȠȎ ȗ ȘȳșȪȘȳȟȠȪ ȟȠȜȞȳțȜȘǦȣȚȎȱȏȡȠȖ ǽȜȕțȎȥȠȓțȜȚȓȞǰȎȦȜȑȜȕȜȦȖȠȎȡȐȳȒȝȜȐȳȒțȜȚȡȚȳȟȤȳȏșȎțȘȎǮȠȎȘ ǵȖȥȖȚȜǰȎȚȡȟȝȳȣȡ ȁȘȞȎȴțȟȪȘȖȗȤȓțȠȞȜȤȳțȬȐȎțțȭȭȘȜȟȠȳȜȟȐȳȠȖ 1 DzǼǰǥDzǸǼǰǥǺǮȀdzǾǥǮǹǶ ȀȎȏșȖȤȭȘȐȎȒȞȎȠȳȐȐȳȒȒȜ DzȓȟȭȠȘȖ 1 2 3 4 0 100 400 1600 1 121 441 1681 2 144 484 1024 1764 3 ǼȒȖțȖȤȳ 4 5 225 576 625 1156 1225 2025 6 256 676 2116 7 8 324 784 1444 2304 361 841 1521 2401 ǮǹDZdzǯǾǮǥǽǼȅǮȀǸǶǮǻǮǹǥǵȁ ȂȜȞȚȡșȖȟȘȜȞȜȥȓțȜȑȜȚțȜȔȓțțȭ ǸȐȎȒȞȎȠțȓȞȳȐțȭțțȭ a2 – b2 = (a – b)(a + b) ax2 + bx + c = 0, a z 0 (a + b)2 = a2 + 2ab + b2 D = b2 – 4ac²ȒȖȟȘȞȖȚȳțȎțȠ (a – b)2 = a2 – 2ab + b2 –b – D –b + D x1 = — , x2 = — ȭȘȧȜD ! 0 2a 2a –b — ȭȘȧȜD = 0 x1 = x2 = 2Ȏ ǺȜȒȡșȪȥȖȟșȎ ~a~ = ax2 + bx + c = a(x – x1)(x – x2) aȭȘȧȜȎ 0, –aȭȘȧȜȎ 0 ǿȠȓȝȓțȳ ǹȜȑȎȞȖȢȚȖ a1 = Ȏ, Ȏn = a a a Ȓșȭa R, n N, n 2 a ! 0, Ȏ z 1, b ! 0, c ! 0, k z 0 nȞȎȕȳȐ a0 ȒȓȎ z 0 aloga b = b a2 = ~Ȏ~ 1 m — a n = n am , Ȏ ! 0, m Z, n N, n y a a =a x+y (ab)x = ax bx Ȏx —y = ax – y Ȏ x Ȏx a – = —x b b logȎ b – c = logȎ b – logȎ c 2 logȎ k b = 1 – logȎ b () k DZȓȜȚȓȠȞȖȥțȎȝȞȜȑȞȓȟȳȭ a 1 + Ȏn Sn = — n 2 ȀȓȜȞȳȭȗȚȜȐȳȞțȜȟȠȓȗ – P (A) = k n logȎ bn = n logȎ b (ax )y = ax y ǮȞȖȢȚȓȠȖȥțȎȝȞȜȑȞȓȟȳȭ an = a1 + d(n – 1) logȎ 1 = 0 logȎ(b c) = logȎ b + logȎ c a–n = — Ȏn ȒșȭȎ z 0, n N x logȎ Ȏ = 1 bn = b1 qn – 1 b (qn– 1) q–1 1 Sn = — , (q z 1) ǸȜȚȏȳțȎȠȜȞȖȘȎ Pn = 1 2 3 n = n! 2 n! — C nk = k! (n – k)! n! A nk = — (n – k)! ǵȎȐȒȎțțȭ²ȳ²ȚȎȬȠȪȐȳȒȝȜȐȳȒțȜȝȜȥȜȠȖȞȖȠȎȝ·ȭȠȪȐȎȞȳȎțȠȳȐȐȳȒȝȜȐȳȒȳ ȕ ȭȘȖȣ șȖȦȓ ȜȒȖț ȝȞȎȐȖșȪțȖȗ ǰȖȏȓȞȳȠȪ ȝȞȎȐȖșȪțȖȗ țȎ ǰȎȦȡ ȒȡȚȘȡ ȐȎȞȳȎțȠȐȳȒȝȜȐȳȒȳȝȜȕțȎȥȠȓȗȜȑȜȐȏșȎțȘȡǮȕȑȳȒțȜȕȳțȟȠȞȡȘȤȳȱȬǻȓȞȜȏȳȠȪ ȳțȦȖȣȝȜȕțȎȥȜȘȡȏșȎțȘȡǮȠȜȚȡȧȜȘȜȚȝ·ȬȠȓȞțȎȝȞȜȑȞȎȚȎȞȓȱȟȠȞȡȐȎȠȖȚȓ ȴȣȭȘȝȜȚȖșȘȖ ǯȡȒȪȠȓȜȟȜȏșȖȐȜȡȐȎȔțȳȝȳȒȥȎȟȕȎȝȜȐțȓțțȭȏșȎțȘȎǮ ǻȓȝȜȑȳȞȦȡȗȠȓȐșȎȟțȜȞȡȥțȜȟȐȜȑȜȞȓȕȡșȪȠȎȠȡțȓȝȞȎȐȖșȪțȜȬȢȜȞȚȜȬȕȎȝȖȟȡȐȳȒȝȜȐȳȒȓȗ 1. ǵȎ ȜȒțȎȘȜȐȖȣ ȘȜțȐȓȞȠȳȐ ȕȎȝșȎȠȖșȖ ȑȞț ǿȘȳșȪȘȖ ȐȟȪȜȑȜ ȠȎȘȖȣ ȘȜțȐȓȞȠȳȐ ȚȜȔțȎȘȡȝȖȠȖȕȎȑȞț" Ǯ ǯ ǰ DZ 6 24 30 36 Ǯ ǯ ǰ DZ 7 4 3 2 ȀȓȚȝȓȞȎȠȡȞȎȜǿ 2. ǻȎ ȑȞȎȢȳȘȡ ȐȳȒȜȏȞȎȔȓțȜ ȕȚȳțȡ ȞȜȏȜȥȜȴ ȠȓȚȝȓȞȎȠȡȞȖ ȒȐȖȑȡțȎ șȓȑȘȜȐȜȑȜ ȎȐȠȜ ȚȜȏȳșȭ ȝȞȜȠȭȑȜȚ ȣȐȖșȖț ȕ ȚȜȚȓțȠȡ ȗȜȑȜ ȕȎȝȡȟȘȡ ǰȖȕțȎȥȠȓ ȕȎ ȑȞȎȢȳȘȜȚ ȘȳșȪȘȳȟȠȪȣȐȖșȖțȝȞȜȠȭȑȜȚȭȘȖȣȞȜȏȜȥȎȠȓȚȝȓȞȎȠȡȞȎȒȐȖȑȡțȎȏȡșȎțȓ ȏȳșȪȦȜȬ ȕȎoǿ 100 90 80 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 ȅȎȟȣȐȖșȖțȖ 3 8 9 10 3. ǽșȎȟȠȖȘȜȐȳ ȘȡșȪȘȖ ȞȎȒȳȡȟȎ ȟȚ ȕȏȓȞȳȑȎȬȠȪ ȡ ȐȖȟȡȐțȳȗ ȦȡȣșȭȒȤȳ ȧȜ ȚȎȱ ȢȜȞȚȡ ȝȞȭȚȜ ȘȡȠțȜȑȜ ȝȎȞȎșȓșȓȝȳȝȓȒȎ ȒȖȐ ȞȖȟȡțȜȘ ȍȘȜȬ ȕ țȎȐȓȒȓțȖȣ ȚȜȔȓ ȏȡȠȖ ȐȖȟȜȠȎ h Ȥȳȱȴ ȦȡȣșȭȒȘȖ" Ǯ ǯ ǰ DZ ȟȚ ȟȚ ȟȚ ȟȚ h 4. ȁȘȎȔȳȠȪȘȜȞȳțȪȞȳȐțȭțțȭ²x Ǯ ǯ ǰ DZ 5 1 –– 5 1 – 5 4 5. ǿȡȚȎȠȞȪȜȣȘȡȠȳȐȝȎȞȎșȓșȜȑȞȎȚȎȒȜȞȳȐțȬȱȜǰȖȕțȎȥȠȓȑȞȎȒȡȟțȡȚȳȞȡȏȳșȪ ȦȜȑȜȘȡȠȎȤȪȜȑȜȝȎȞȎșȓșȜȑȞȎȚȎ Ǯ 100 ǯ o 80 o ǰ 140 4 DZ o 40 Dz o 120o 3m – 2n 8 3m 8 6. ǿȝȞȜȟȠȳȠȪȐȖȞȎȕ — – — Ǯ ǯ ǰ DZ Dz n –– 4 n –– 8 n –– 6 m –– 4 3m – n — 4 7. ȁȘȎȔȳȠȪȕȝȜȚȳȔțȎȐȓȒȓțȖȣȓȟȘȳȕȑȞȎȢȳȘȎȢȡțȘȤȳȴy = –2x Ǯ ǯ y ǰ y x 0 DZ y x 0 Dz y x 0 y 0 x x 0 8. Dzșȭ ȚȳȟȤȓȐȜȟȠȳ ȧȜ șȓȔȖȠȪ țȎ ȞȳȐțȳ ȚȜȞȭ țȜȞȚȎșȪțȖȗ ȎȠȚȜȟȢȓȞțȖȗ ȠȖȟȘ ȟȠȎțȜȐȖȠȪȚȚȞȠȟȠǥȕȝȳȒțȭȠȠȭȚțȎȘȜȔțȳȚȓȠȞȳȐȡȑȜȞȡȎȠȚȜȟȢȓȞțȖȗ ȠȖȟȘ ȕțȖȔȡȱȠȪȟȭ țȎ ȚȚ ȞȠ ȟȠ ȁȘȎȔȳȠȪ ȕȝȜȚȳȔ țȎȐȓȒȓțȖȣ ȢȜȞȚȡșȡ ȕȎ ȭȘȜȬ ȐȖȕțȎȥȎȬȠȪ ȎȠȚȜȟȢȓȞțȖȗ ȠȖȟȘ Ȟ ȡ ȚȚ ȞȠ ȟȠ țȎ ȐȖȟȜȠȳ h ȚȓȠȞȳȐ țȎȒ ȞȳȐțȓȚȚȜȞȭ Ǯ ǯ à p= — p = 760 – 100h — 10h ǰ 10 DZ — p = 760 + 10h 100 5 Dz — p = 760 – 10h p = 760 + 100h — 10 100 ȍȘȳȕțȎȐȓȒȓțȖȣȠȐȓȞȒȔȓțȪȱȝȞȎȐȖșȪțȖȚȖ" ǥ ǻȎȐȘȜșȜȏȡȒȪȭȘȜȑȜȞȜȚȏȎȚȜȔțȎȜȝȖȟȎȠȖȘȜșȜ ǥǥ DzȳȎȑȜțȎșȳȏȡȒȪȭȘȜȑȜȞȜȚȏȎȐȕȎȱȚțȜȝȓȞȝȓțȒȖȘȡșȭȞțȳ ǥǥǥ ȁȏȡȒȪȭȘȜȚȡȞȜȚȏȳȐȟȳȟȠȜȞȜțȖȞȳȐțȳ Ǯ ǯ ǰ DZ Dz șȖȦȓǥȠȎǥǥ șȖȦȓǥȠȎǥǥ, șȖȦȓǥ, șȖȦȓǥǥȠȎǥǥ, ǥǥǥȠȎǥǥǥ 10. ȁȘȎȔȳȠȪȝȞȜȚȳȔȜȘȭȘȜȚȡțȎșȓȔȖȠȪȘȜȞȳțȪȞȳȐțȭțțȭx Ǯ ǯ ǰ DZ Dz [–12; –6) [–6; 0) [0; 6) [6; 12) [12; + 11. ȍȘȎȕțȎȐȓȒȓțȖȣȢȡțȘȤȳȗȱȝȓȞȐȳȟțȜȬȒșȭȢȡțȘȤȳȴf(x) = x–4 " Ǯ ǯ 1 F(x) = – —5 F(x) = – —5 5x ǰ 3 x DZ 4 x F(x) = – —5 6 Dz 5 x F(x) = – —5 1 F(x) = – —3 3x 54 Ã4 20 12. ǼȏȥȖȟșȳȠȪ — 3 Ǯ ǯ ǰ DZ Dz 5 – 4 1 — 10 1 – 2 1 — 20 10 13. ǾȜȕȐ·ȭȔȳȠȪțȓȞȳȐțȳȟȠȪORJ (3x) ! Ǯ ǯ ǰ DZ Dz ² ² (0,27; + (0,6; + (0; 0,27) Ǯ ǯ ǰ DZ Dz 2sin2 x 4sin2 x 4sin2 x cos2 x 2sin2 x cos2 x sin4x2 14. sin2 2x = 7 15. ǿ ȠȜȞȜțȎ ȜȟțȜȐȖ ȝȞȎȐȖșȪțȜȴ ȥȜȠȖȞȖȘȡȠțȜȴ ȝȳȞȎȚȳȒȖ ȒȜȞȳȐțȬȱ ȟȚ ȎȝȜȢȓȚȎ ² ȟȚǰȖȕțȎȥȠȓȝșȜȧȡȝȜȐțȜȴȝȜȐȓȞȣțȳȤȳȱȴȝȳȞȎȚȳȒȖ Ǯ ǯ 2 ȟȚ ǰ ȟȚ 2 ȟȚ DZ 2 ȟȚ Dz 2 ȟȚ2 ǽȞȭȚȜșȳțȳȗțȜȬ ȒȜȞȜȑȜȬ Ǯǰ ȞȡȣȎȱȠȪȟȭ ȠȞȜșȓȗȏȡȟ ȒȖȐ ȞȖȟȡțȜȘ ǹȳțȳȭ CD ȓșȓȘȠȞȖȥțȜȑȜ ȒȞȜȠȡ ȝȎȞȎșȓșȪțȎ Ǯǰ ȗ ȒȎȣȡ MN ȠȞȜșȓȗȏȡȟȎ ȆȠȎțȑȎ KN, ȧȜ țȎ ȞȖȟȡțȘȡ ȱ ȐȳȒȞȳȕȘȜȚ ȡȠȐȜȞȬȱ ȕ ǺN ȘȡȠ ǰȳȒȟȠȎțȳ ȚȳȔ ȝȞȭȚȖȚȖ CD ȗ Ǯǰ, ǺN ȗ Ǯǰ ȒȜȞȳȐțȬȬȠȪ Ț ȳ Ț ȐȳȒȝȜȐȳȒțȜ ȁȘȎȔȳȠȪ ȝȞȜȚȳȔȜȘ ȭȘȜȚȡ țȎșȓȔȖȠȪ ȒȜȐȔȖțȎ ȡ Ț ȦȠȎțȑȖ KN ȁȐȎȔȎȗȠȓ ȧȜ Ȑȟȳ ȕȎȕțȎȥȓțȳ ȝȞȭȚȳ șȓȔȎȠȪȐȜȒțȳȗȝșȜȧȖțȳ ǿ K D N Ț Ț 30Ȝ M A B Ǯ ǯ ǰ DZ Dz [1; 3) [3; 5) [5; 5,5) [5,5; 6) [6; 8) 8 ȁȕȎȐȒȎțțȭȣ²ȒȜȘȜȔțȜȑȜȕȠȞȪȜȣȞȭȒȘȳȐȳțȢȜȞȚȎȤȳȴȝȜȕțȎȥȓțȖȣȤȖȢ ȞȎȚȖȒȜȏȓȞȳȠȪȜȒȖțȝȞȎȐȖșȪțȖȗțȎǰȎȦȡȒȡȚȘȡȐȎȞȳȎțȠȝȜȕțȎȥȓțȖȗȏȡȘ ȐȜȬ ǽȜȟȠȎȐȠȓ ȝȜȕțȎȥȘȖ Ȑ ȠȎȏșȖȤȭȣ ȐȳȒȝȜȐȳȒȓȗ ȒȜ ȕȎȐȒȎțȪ ȡ ȏșȎțȘȡ Ǯ țȎ ȝȓȞȓȠȖțȳȐȳȒȝȜȐȳȒțȖȣȞȭȒȘȳȐ ȤȖȢȞȖ ȳȘȜșȜțȜȘ ȏȡȘȐȖ ȁȟȳȳțȦȳȐȖȒȖǰȎȦȜȑȜ ȕȎȝȖȟȡȐȏșȎțȘȡǮȘȜȚȝ·ȬȠȓȞțȎȝȞȜȑȞȎȚȎȞȓȱȟȠȞȡȐȎȠȖȚȓȭȘȝȜȚȖșȘȖ ǯȡȒȪȠȓȜȟȜȏșȖȐȜȡȐȎȔțȳȝȳȒȥȎȟȕȎȝȜȐțȓțțȭȏșȎțȘȎǮ ǻȓȝȜȑȳȞȦȡȗȠȓȐșȎȟțȜȞȡȥțȜȟȐȜȑȜȞȓȕȡșȪȠȎȠȡțȓȝȞȎȐȖșȪțȜȬȢȜȞȚȜȬȕȎȝȖȟȡȐȳȒȝȜȐȳȒȓȗ 17. ȁȟȠȎțȜȐȳȠȪ ȐȳȒȝȜȐȳȒțȳȟȠȪ ȚȳȔ ȑȞȎȢȳȘȜȚ ² ȢȡțȘȤȳȴ ȐȖȕțȎȥȓțȜȴ țȎ ȝȞȜ ȚȳȔȘȡ>²@ȠȎȴȴȐșȎȟȠȖȐȳȟȠȬ Ǯ²Dz DZȞȎȢȳȘ ȢȡțȘȤȳȴ y y y y = f (x) y = f (x) 1 –4 0 1 4 y = f (x) 1 x –4 0 1 1 4 1 x 2 –4 01 4 x 3 ǰșȎȟȠȖȐȳȟȠȪ ȢȡțȘȤȳȴ Ǯ ǯ ǰ DZ Dz ȢȡțȘȤȳȭȱțȓȝȎȞțȜȬ țȎȗȚȓțȦȓȕțȎȥȓțțȭȢȡțȘȤȳȴțȎȝȞȜȚȳȔȘȡ>@ ȒȜȞȳȐțȬȱ ȢȡțȘȤȳȭȱȝȎȞțȜȬ ȑȞȎȢȳȘȢȡțȘȤȳȴțȓȚȎȱȟȝȳșȪțȖȣȠȜȥȜȘȳȕȑȞȎȢȳȘȜȚ ȞȳȐțȭțțȭ x – 3)2 + (y – 4)2 = 4 ȑȞȎȢȳȘȢȡțȘȤȳȴȠȞȖȥȳȝȓȞȓȠȖțȎȱȝȞȭȚȡy = 1 ǮǯǰDZDz 1 2 3 ȁȟȠȎțȜȐȳȠȪ ȐȳȒȝȜȐȳȒțȳȟȠȪ ȚȳȔ ȐȖȞȎȕȜȚ ² ȳ ȠȐȓȞȒȔȓțțȭȚ ȝȞȜ ȗȜȑȜ ȕțȎȥȓț – țȭ Ǯ²Dz ȭȘȓȱȝȞȎȐȖșȪțȖȚȭȘȧȜa = –2 1 3 ǰȖȞȎȕ ȀȐȓȞȒȔȓțțȭ ȝȞȜ ȕțȎȥȓțțȭ ȐȖȞȎȕȡ 1 a2 Ǯ ȏȳșȪȦȓȐȳȒ 2 a + ~a~ 3 log5 5a ǯ țȎșȓȔȖȠȪȝȞȜȚȳȔȘȡ ǰ ȱȐȳȒ·ȱȚțȖȚȥȖȟșȜȚ ǮǯǰDZDz 1 2 3 DZ țȎșȓȔȖȠȪȝȞȜȚȳȔȘȡ> Dz ȒȜȞȳȐțȬȱ Ǹ ȐȎȒȞȎȠ ǮǰǿD ȗ ȝȞȭȚȜȘȡȠțȎ ȠȞȎȝȓȤȳȭ ǰMNǿ șȓȔȎȠȪ Ȑ ȜȒțȳȗ ȝșȜȧȖțȳ ȒȖȐ ȞȖȟȡțȜȘ ǽșȜȧȎ ȘȜȔțȜȴ ȳȕ ȤȖȣ ȢȳȑȡȞȒȜȞȳȐțȬȱȟȚ2, ǮǺ ȟȚ ȁȟȠȎțȜȐȳȠȪ ȐȳȒȝȜȐȳȒțȳȟȠȪ ȚȳȔ ȐȳȒȞȳȕȘȜȚ ² ȳ ȗȜȑȜ ȒȜȐȔȖțȜȬ Ǯ²Dz M N B C A D ǰȳȒȞȳȕȜȘ DzȜȐȔȖțȎ ȐȳȒȞȳȕȘȎ 1 ȟȠȜȞȜțȎȘȐȎȒȞȎȠȎǮǰǿD 2 ȐȖȟȜȠȎȠȞȎȝȓȤȳȴǰMNǿ 3 ȚȓțȦȎȜȟțȜȐȎȠȞȎȝȓȤȳȴǰMNǿ Ǯ ǯ ǰ DZ Dz 10 ȟȚ ȟȚ ȟȚ ȟȚ ȟȚ ǮǯǰDZDz 1 2 3 20. ǻȎ ȞȖȟȡțȘȡ ȕȜȏȞȎȔȓțȜ ȝȞȭȚȜȘȡȠțȖȗ ȝȎȞȎ șȓșȓȝȳȝȓȒ ABCDA1B1C1D1 ȡ ȭȘȜȚȡ AB = 3, AD = 4, AA1 ȁȐȳȒȝȜȐȳȒțȳȠȪ ȝȜȥȎȠȜȘ Ȟȓȥȓț A 1 țȭ ² ȳȕ ȗȜȑȜ ȕȎȘȳțȥȓțțȭȚ Ǯ ² Dz ȠȎȘ ȧȜȏ ȡȠȐȜȞȖșȜȟȭȝȞȎȐȖșȪțȓȠȐȓȞȒȔȓțțȭ B1 A ǽȜȥȎȠȜȘ Ȟȓȥȓțțȭ 1 2 3 C1 D1 B C D ǵȎȘȳțȥȓțțȭ Ȟȓȥȓțțȭ ǰȳȒȟȠȎțȪȐȳȒȠȜȥȘȖǿȒȜȝșȜȧȖțȖ ǮǮ1ǰ1 ȒȜȞȳȐțȬȱ ǰȳȒȟȠȎțȪȐȳȒȠȜȥȘȖAȒȜȝȞȭȚȜȴCC1ȒȜȞȳȐțȬȱ ǰȳȒȟȠȎțȪȚȳȔȝșȜȧȖțȎȚȖ ABC ȳ Ǯ1ǰ1C1 ȒȜȞȳȐțȬȱ ǮǯǰDZDz Ǯ ǯ ǰ DZ Dz 1 2 3 11 ǾȜȕȐ·ȭȔȳȠȪȕȎȐȒȎțțȭ²ǼȒȓȞȔȎțȳȥȖȟșȜȐȳȐȳȒȝȜȐȳȒȳȕȎȝȖȦȳȠȪȡȕȜȦȖȠȳ ȠȎ ȏșȎțȘȡ Ǯ ǰȳȒȝȜȐȳȒȪ ȕȎȝȖȟȡȗȠȓ șȖȦȓ ȒȓȟȭȠȘȜȐȖȚ ȒȞȜȏȜȚ ȡȞȎȣȡȐȎȐȦȖ ȝȜșȜȔȓțțȭ ȘȜȚȖ ȝȜ ȜȒțȳȗ ȤȖȢȞȳ Ȑ ȘȜȔțȳȗ ȘșȳȠȖțȤȳ ȐȳȒȝȜȐȳȒțȜ ȒȜ ȕȞȎȕȘȳȐ țȎȐȓȒȓțȖȣȡȏșȎțȘȡǮ 21. Ǽ șȓțȎ ȘȡȝȖșȎ ȥȓȞȓȕ ȐȓȏȟȎȗȠ ȝȜȟȎȒȜȥțȖȗ ȒȜȘȡȚȓțȠ ȒȖȐ ȢȞȎȑȚȓțȠ ȒȜȘȡȚȓțȠȎ țȎ ȝȜȠȭȑ ȧȜ ȘȜȦȠȡȱ ȑȞț ȁ ȗȜȑȜ ȐȎȞȠȳȟȠȪ ȐȣȜȒȭȠȪ ȐȎȞȠȜȟȠȳ ȘȐȖȠȘȎ ² ȑȞț ȝșȎȤȘȎȞȠȖ ² ȑȞț ȗ ȳțȦȖȣ ȐȖȠȞȎȠ ² ȑȞț ǵȎ ȑȜȒȖț ȒȜ ȐȳȒȝȞȎȐșȓțțȭ ȝȜȠȭȑȎ ǼșȓțȎ ȐȖȞȳȦȖșȎ ȝȜȐȓȞțȡȠȖ Ȥȓȗ ȝȜȟȎȒȜȥțȖȗ ȒȜȘȡȚȓțȠ ǰȳȒȝȜȐȳȒțȜ ȒȜ ȝȞȎȐȖș ȕȎ ȠȎȘȖȣ ȡȚȜȐ ȴȗ ȝȜȐȓȞȠȎȬȠȪ șȖȦȓ ȐȎȞȠȳȟȠȪ ȘȐȖȠȘȎ ȗ ȝȜșȜȐȖțȡ ȐȎȞȠȜȟȠȳ ȝșȎȤȘȎȞȠȖ ǸȞȳȚ ȠȜȑȜ ȕȎ ȝȜȐȓȞțȓțțȭ ȝȜȟȎȒȜȥ țȜȑȜȒȜȘȡȚȓțȠȎȕǼșȓțȖȒȜȒȎȠȘȜȐȜȟȠȭȑțȡȠȪȕȏȳȞȑȞț ǬǯDZ ɐȿɃɉɈɋȺȾɈɑɇɂɃȾɈɄɍɆȿɇɌȯɉȱȾɋɌȺȼɈɘȾɅəɉɊɈȲɁȾɍ ǯȤȻțȖȜȭșřȇȠŨȳ ǠȕȖȗȘșȝȞȢǮȟșȡȔ ǯȢȼțȘ ǢȻȘȣȤȔȖȟșȡȡȳ 2200001 ǪǨȈǢŞǯǠDZǠǦǨǰDZǼǪǨǩ ǢȔȗȢȡ ǯȤȜțȡȔȫșȡȡȳ 2200200 ǢȇǭǭǨǶǿ ǬȻȥȪș ǤȔȦȔŵȫȔȥȖȻȘȣȤŜ 12.12.2020 06:50 ǤȔȦȔŵȫȔȥȣȤȜȕŜ 12.12.2020 09:09 DZșȤȖȻȥ ǢǠǰDzʰ240,00ǣǰǭ 1. ȍȘȡȟȡȚȡȑȞȜȦȓȗǾ ȡȑȞț ȜȠȞȖȚȎȱǼșȓțȎȝȜȐȓȞțȡȐȦȖȤȓȗȒȜȘȡȚȓțȠ" ǰȳȒȝȜȐȳȒȪ 2. ǿȘȳșȪȘȖȐȳȒȟȜȠȘȳȐȐȳȒȐȎȞȠȜȟȠȳȒȜȘȡȚȓțȠȎȟȠȎțȜȐȖȠȪȟȡȚȎȑȞȜȦȓȗǾ" ǰȳȒȝȜȐȳȒȪ 12 22. ǻȎ ȞȖȟȡțȘȡ ȕȜȏȞȎȔȓțȜ ȝȞȭȚȜȘȡȠțȖȘ ABCD ȗ ȘȜșȜ ȭȘȓ ȒȜȠȖȘȎȱȠȪȟȭ ȒȜ ȟȠȜȞȜțȖ Ǯǰ ȗ ȟȠȜȞȳț ǰǿ ȗ ǮD Ȑ ȠȜȥȘȎȣ M ȳ K ȐȳȒȝȜȐȳȒțȜ ǽȓȞȖȚȓȠȞ ȥȜȠȖȞȖȘȡȠțȖȘȎ ǮǰǺK ȒȜȞȳȐțȬȱȟȚȎȒȜȐȔȖțȎȐȳȒȞȳȕȘȎKǿ²ȟȚ 1. ǰȖȕțȎȥȠȓȞȎȒȳȡȟ ȡȟȚ ȕȎȒȎțȜȑȜȘȜșȎ ǰȳȒȝȜȐȳȒȪ 2. ǼȏȥȖȟșȳȠȪȝșȜȧȡ ȡȟȚ2 ȝȞȭȚȜȘȡȠțȖȘȎABCD ǰȳȒȝȜȐȳȒȪ 13 B M C A K D ń 23. ȁ ȝȞȭȚȜȘȡȠțȳȗ ȟȖȟȠȓȚȳ ȘȜȜȞȒȖțȎȠ ȡ ȝȞȜȟȠȜȞȳ ȕȎȒȎțȜ ȐȓȘȠȜȞ AB(–3; 8; 1) ȳȠȜȥȘȡǰ ² ȠȜȥȘȎǼ²ȝȜȥȎȠȜȘȘȜȜȞȒȖțȎȠ 1. ǰȖȕțȎȥȠȓȜȞȒȖțȎȠȡyȠȜȥȘȖ A(x; y; z ǰȳȒȝȜȐȳȒȪ ń ń 2. ǼȏȥȖȟșȳȠȪȟȘȎșȭȞțȖȗȒȜȏȡȠȜȘOAÃAB ǰȳȒȝȜȐȳȒȪ 14 ǮȞȖȢȚȓȠȖȥțȡȝȞȜȑȞȓȟȳȬ an ȕȎȒȎțȜȢȜȞȚȡșȜȬnȑȜȥșȓțȎan = 2,6n² 1. ǰȖȕțȎȥȠȓȟȪȜȚȖȗȥșȓțȤȳȱȴȝȞȜȑȞȓȟȳȴ ǰȳȒȝȜȐȳȒȪ 2. ǰȖȕțȎȥȠȓȞȳȕțȖȤȬa4 – a1 ǰȳȒȝȜȐȳȒȪ 15 25. ȁ ȝȓȞȦȜȚȡ ȘșȎȟȳ ȒȳȐȥȎȠȜȘ ȕ ȭȘȖȣ șȖȦȓ ȜȒțȎ țȎ ȳȚ·ȭ DzȎȞȖțȎȳ ȣșȜȝȥȖ ȘȳȐ ǻȎ ȝȓȞȦȜȚȡ ȡȞȜȤȳ ȐȥȖȠȓșȪȘȎ țȎȐȚȎțțȭ ȢȜȞȚȡȱ ȝȎȞȖ ȒȳȠȓȗ ȭȘȳ ȟȖȒȳȠȖ ȚȡȠȪȕȎȜȒțȳȱȬȝȎȞȠȜȬǽȓȞȦȜȬȐȜțȎȐȖȏȖȞȎȱȝȎȞȡȒșȭDzȎȞȖțȖȍȘȎȗȚȜȐȳȞțȳȟȠȪ ȠȜȑȜȧȜDzȎȞȖțȎȟȖȒȳȠȖȚȓȕȎȜȒțȳȱȬȝȎȞȠȜȬȕȒȳȐȥȖțȘȜȬ" ǰȳȒȝȜȐȳȒȪ Dzșȭ ȝȞȖȑȜȠȡȐȎțțȭ ȒȓȕȳțȢȳȘȡȐȎșȪțȜȑȜ ȞȜȕȥȖțȡ ȘȜțȤȓțȠȞȎȠ ȞȜȕȐȜȒȭȠȪ ȐȜȒȜȬ Ȑ ȚȎȟȜȐȜȚȡ ȐȳȒțȜȦȓțțȳ ȐȳȒȝȜȐȳȒțȜ ȝȳȟșȭ ȥȜȑȜ țȎ ȘȜȔțȳ ȑ ȐȜȒȖ ȒȜȏȎȐ șȭȬȠȪ ȑ ȎȞȜȚȎȠȖȥțȜȴ ȞȳȒȖțȖ ǿȘȳșȪȘȖ ȑȞȎȚȳȐ ȘȜțȤȓțȠȞȎȠȡ ȝȜȠȞȳȏțȜ Ȓșȭ ȝȞȖȑȜȠȡȐȎțțȭȑȞȜȕȥȖțȡ" ǰȳȒȝȜȐȳȒȪ 16 27. ǼȏȥȖȟșȳȠȪȕțȎȥȓțțȭȐȖȞȎȕȡa2 – 24a + 16 – 3 27a3ȕȎȎ ǰȳȒȝȜȐȳȒȪ 28. ǾȜȕȐ·ȭȔȳȠȪ ȞȳȐțȭțțȭ x4 – x2 ² ȁ ȐȳȒȝȜȐȳȒȳ ȕȎȝȖȦȳȠȪ ȒȜȏȡȠȜȘ ȡȟȳȣ ȗȜȑȜ ȒȳȗȟțȖȣȘȜȞȓțȳȐ ǰȳȒȝȜȐȳȒȪ ǾȓȒȎȘȠȜȞ ȟȠȞȳȥȘȖ țȜȐȖț ȐȖȞȳȦȡȱ ȡ ȭȘȳȗ ȝȜȟșȳȒȜȐțȜȟȠȳ ȞȜȕȚȳȟȠȖȠȖ ȞȳȕțȖȣ țȜȐȖț ȝȜșȳȠȖȥțȳ ȟȡȟȝȳșȪțȳ ȗ ȟȝȜȞȠȖȐțȡ ǿȘȳșȪȘȖ ȐȟȪȜȑȜ ȱ ȞȳȕțȖȣ ȝȜȟșȳȒȜȐțȜȟȠȓȗ ȞȜȕȚȳȧȓțțȭ ȤȖȣ țȜȐȖț ȡ ȟȠȞȳȥȤȳ ȕȎ ȡȚȜȐȖ ȧȜ ȝȜșȳȠȖȥțȳ țȜȐȖțȖȚȎȬȠȪȝȓȞȓȒȡȐȎȠȖȳțȦȖȚȎȟȝȜȞȠȖȐțȎțȜȐȖțȎ²ȏȡȠȖȜȟȠȎțțȪȜȬ"ȁȐȎ ȔȎȗȠȓȧȜȘȜȔțȡȳȕȤȖȣțȜȐȖțȡȟȠȞȳȥȤȳțȓȝȜȐȠȜȞȬȬȠȪ ǰȳȒȝȜȐȳȒȪ 17 ǾȜȕȐ·ȭȔȳȠȪ ȕȎȐȒȎțțȭ ǵȎȝȖȦȳȠȪ ȡ ȏșȎțȘȡ ǯ ȝȜȟșȳȒȜȐțȳ șȜȑȳȥțȳ Ȓȳȴ ȠȎ ȝȜȭȟțȓțțȭ Ȑȟȳȣ ȓȠȎȝȳȐ ȞȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ȕȞȜȏȳȠȪ ȝȜȟȖșȎțțȭ țȎ ȚȎȠȓȚȎȠȖȥțȳȢȎȘȠȖȕȭȘȖȣȐȖȝșȖȐȎȱȠȓȥȖȳțȦȓȠȐȓȞȒȔȓțțȭȍȘȧȜȝȜȠȞȳȏțȜ ȝȞȜȳșȬȟȠȞȡȗȠȓȞȜȕȐ·ȭȕȎțțȭȕȎȐȒȎțȪȞȖȟȡțȘȎȚȖȑȞȎȢȳȘȎȚȖȠȜȧȜ 30. ǵȎȒȎțȜȢȡțȘȤȳȬy = x3 – 3x 1. Dz șȭ țȎȐȓȒȓțȖȣ ȡ ȠȎȏșȖȤȳ ȕțȎȥȓțȪ ȎȞȑȡȚȓțȠȎ ȣ ȐȖȕțȎȥȠȓ ȐȳȒȝȜȐȳȒțȳ ȴȚ ȕțȎȥȓțțȭȡ x 0 –1 2 y 2. ǰȖȕțȎȥȠȓȗȕȎȝȖȦȳȠȪȘȜȜȞȒȖțȎȠȖȠȜȥȜȘȝȓȞȓȠȖțȡȑȞȎȢȳȘȎȢȡțȘȤȳȴy = x3 – 3x ȳȕȐȳȟȟȬȣ 3. ǵțȎȗȒȳȠȪȝȜȣȳȒțȡf c ȢȡțȘȤȳȴf (x) = x3 – 3x 4. ǰȖȕțȎȥȠȓțȡșȳȢȡțȘȤȳȴf c 5. ǰ ȖȕțȎȥȠȓȝȞȜȚȳȔȘȖȕȞȜȟȠȎțțȭȳȟȝȎȒȎțțȭȠȜȥȘȖȓȘȟȠȞȓȚȡȚȡȗȓȘȟȠȞȓȚȡȚȖ ȢȡțȘȤȳȴf 6. ǽȜȏȡȒȡȗȠȓȓȟȘȳȕȑȞȎȢȳȘȎȢȡțȘȤȳȴf ǰȳȒȝȜȐȳȒȪ 18 31. ǼȟȪȜȐȖȚ ȝȓȞȓȞȳȕȜȚ ȤȖșȳțȒȞȎ ȱ ȝȞȭȚȜȘȡȠțȖȘ ǮǰǿD ȟȠȜȞȜțȎ ǮD ȭȘȜȑȜ șȓȔȖȠȪ Ȑ țȖȔțȳȗ ȜȟțȜȐȳ ȤȖșȳțȒȞȎ DzȳȎȑȜțȎșȪ Ǯǿ ȝȓȞȓȞȳȕȡ ȒȜȞȳȐțȬȱ d ȗ ȡȠȐȜȞȬȱ ȕ ȝșȜȧȖțȜȬțȖȔțȪȜȴȜȟțȜȐȖȤȖșȳțȒȞȎȘȡȠᇗ 1. ǵȜȏȞȎȕȳȠȪțȎȞȖȟȡțȘȡȕȎȒȎțȖȗȤȖșȳțȒȞȳȗȜȑȜȜȟȪȜȐȖȗȝȓȞȓȞȳȕǮǰǿD 2. ȁȘȎȔȳȠȪȘȡȠᇗȧȜȡȠȐȜȞȬȱȝȞȭȚȎǮǿȳȕȝșȜȧȖțȜȬțȖȔțȪȜȴȜȟțȜȐȖȤȖșȳțȒȞȎ 3. ǰȖȕțȎȥȠȓȜȏ·ȱȚȤȖșȳțȒȞȎ ǰȳȒȝȜȐȳȒȪ ǾȜȕȐ·ȭȔȳȠȪ ȕȎȐȒȎțțȭ ² ǵȎȝȖȦȳȠȪ ȡ ȏșȎțȘȡ ǰ ȝȜȟșȳȒȜȐțȳ șȜȑȳȥțȳ Ȓȳȴ ȠȎ ȝȜȭȟțȓțțȭ Ȑȟȳȣ ȓȠȎȝȳȐ ȞȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ȕȞȜȏȳȠȪ ȝȜȟȖșȎțțȭ țȎ ȚȎȠȓȚȎȠȖȥțȳȢȎȘȠȖȕȭȘȖȣȐȖȝșȖȐȎȱȠȓȥȖȳțȦȓȠȐȓȞȒȔȓțțȭȍȘȧȜȝȜȠȞȳȏțȜ ȝȞȜȳșȬȟȠȞȡȗȠȓȞȜȕȐ·ȭȕȎțțȭȕȎȐȒȎțȪȞȖȟȡțȘȎȚȖȑȞȎȢȳȘȎȚȖȠȜȧȜ ȁȐȎȑȎȁȚȜȐȖȕȎȐȒȎțȪȳȚȎȬȠȪȟȝȳșȪțȡȥȎȟȠȖțȡǾȜȕȐ·ȭȕȎțțȭȕȎȐȒȎțȪ ²ȕȎȝȖȦȳȠȪșȖȦȓȐȏșȎțȘȡǰ. 32. Ǽ ȟȪȜȐȖȚ ȝȓȞȓȞȳȕȜȚ ȤȖșȳțȒȞȎ ȱ ȝȞȭȚȜȘȡȠțȖȘ ǮǰǿD ȟȠȜȞȜțȎ ǮD ȭȘȜȑȜ șȓȔȖȠȪ ȡ țȖȔțȳȗ ȜȟțȜȐȳ ȤȖșȳțȒȞȎ DzȳȎȑȜțȎșȪ Ǯǿ ȝȓȞȓȞȳȕȡ ȒȜȞȳȐțȬȱ d ȗ ȡȠȐȜȞȬȱ ȕ ȝșȜȧȖțȜȬ țȖȔțȪȜȴ ȜȟțȜȐȖ ȤȖșȳțȒȞȎ ȘȡȠ ᇗ ǻȎ ȘȜșȳ țȖȔțȪȜȴ ȜȟțȜȐȖ ȐȖȏȞȎțȜ ȠȜȥȘȡKȠȎȘȧȜȑȞȎȒȡȟțȎȚȳȞȎȒȡȑȖǮKȒȜȞȳȐțȬȱ 1. ǵ ȜȏȞȎȕȳȠȪ țȎ ȞȖȟȡțȘȡ ȕȎȒȎțȖȗ ȤȖșȳțȒȞ ȳ ȐȘȎȔȳȠȪ ȘȡȠ Ȗ ȚȳȔ ȝșȜȧȖțȜȬ (KBD ȳȝșȜȧȖțȜȬțȖȔțȪȜȴȜȟțȜȐȖȤȖșȳțȒȞȎǼȏȽȞȡțȠȡȗȠȓȗȜȑȜȝȜșȜȔȓțțȭ 2. ǰȖȕțȎȥȠȓȘȡȠȖ ǰȳȒȝȜȐȳȒȪ 2a2 + 5a – 3 1 – 2a —o 33. DzȜȐȓȒȳȠȪȠȜȠȜȔțȳȟȠȪ — = 2cos240 a+3 20 34. ǵȎȒȎțȜȟȖȟȠȓȚȡȞȳȐțȭțȪ ax 2 + 3ax + 41 + xà y = 1, y = 8, Ȓȓx, y²ȕȚȳțțȳa²ȒȜȐȳșȪțȎȟȠȎșȎ 1. ǾȜȕȐ·ȭȔȳȠȪȟȖȟȠȓȚȡȭȘȧȜa 2. ǰȖȕțȎȥȠȓȐȟȳȞȜȕȐ·ȭȕȘȖȕȎȒȎțȜȴȟȖȟȠȓȚȖȕȎșȓȔțȜȐȳȒȕțȎȥȓțȪa 21 ǰȳȒȝȜȐȳȒȪ 22 ǽȜȣȳȒțȎȢȡțȘȤȳȴ ǽȓȞȐȳȟțȎȢȡțȘȤȳȴ ȠȎȐȖȕțȎȥȓțȖȗȳțȠȓȑȞȎș ǿ, Ĵ²ȟȠȎșȳ (ǿ)Ļ = 0 ȣĻ = 1 (ȣ Ĵ)Ļ Ĵx Ĵ² 1 ( x )Ļ = – 2 x (e x )Ļ = e x 1 (ln x)Ļ = – x (sin x)Ļ = cos x (cos x)Ļ = – sin x 1 – (tg x)Ļ = cos 2x (u + v)Ļ = uĻ + vĻ (u – v)Ļ = uĻ – vĻ (uv)Ļ = uĻv + uvĻ (Cu)Ļ = CuĻ Ļ ȂȡțȘȤȳȭf(x) ǵȎȑȎșȪțȖȗȐȖȑșȭȒ ȝȓȞȐȳȟțȖȣF(x) + C, C²ȒȜȐȳșȪțȎȟȠȎșȎ 0 C x+C 1 xĴĴz –1 x— +C Ĵ 1 – x ln ~x~ + C ex sin x ex + C –cos x + C cos x sin x + C 1 — cos2 x tg x + C Ļ v – uv (u–v)Ļ = u– v 2 b Ĵ +1 b f(x)dx = F(x)~a = F(b) – F(a ²ȢȜȞȚȡșȎǻȪȬȠȜțȎ²ǹȓȗȏțȳȤȎ a ȀȞȖȑȜțȜȚȓȠȞȳȭ sin Ĵ = yĴ cos Ĵ = xĴ sin2 Ĵ + cos2 Ĵ = 1 M(xĴ, yĴ ) 1 VLQĴ tg Ĵ = – FRVĴ 1 – 1 + tg2 Ĵ = cos 2Ĵ sin2Ĵ = 2sin Ĵcos Ĵ cos2Ĵ = cos2 Ĵ²sin2 Ĵ o VLQ Ĵ) = cos Ĵ o FRV Ĵ) = – sin Ĵ 1 WJ o Ĵ) = – – tgĴ y yĴ Ĵ o sin(180 ²Ĵ) = sin Ĵ o cos(180 ²Ĵ) = – cos Ĵ –1 xĴ 1 0 tg(180o ²Ĵ) = – tg Ĵ –1 ȀȎȏșȖȤȭȕțȎȥȓțȪȠȞȖȑȜțȜȚȓȠȞȖȥțȖȣȢȡțȘȤȳȗȒȓȭȘȖȣȘȡȠȳȐ D ȞȎȒ 0 ȑȞȎȒ 0 o ʌ – 6 30 o ʌ – 4 ʌ – 3 45o 60 o ʌ – 2 ʌ 3ʌ — 2 2ʌ o 180o 270o 360o sin D 0 1 – 2 —2 2 —3 2 1 0 –1 0 cos D 1 —3 2 —2 2 1 – 2 0 –1 0 1 tg D 0 1 — 3 1 țȓȳȟțȡȱ 0 țȓȳȟțȡȱ 0 3 23 x DZdzǼǺdzȀǾǥȍ DzȜȐȳșȪțȖȗȠȞȖȘȡȠțȖȘ a+b+c p=— 2 Ȗ b ha Į A c a a2 = b2 + c2 – 2bc cos Ĵ ȕ a b c — =—=— = 2R VLQĴ sinȕ sinȖ B 1 ȅȜȠȖȞȖȘȡȠțȖȘȖ ǸȜșȜ Ǽȏ·ȱȚțȳȢȳȑȡȞȖȗȠȳșȎ b – c = cos Ĵ 1 ǽȎȞȎșȓșȜȑȞȎȚ Į b ǾȜȚȏ ȀȞȎȝȓȤȳȭ b d1 b Ȗ c S = p(p – a)(p – b)(p – c) ǽȞȭȚȜȘȡȠțȖȘ ha a a = tg Ĵ – c = sin Ĵ– b a R – ȞȎȒȳȡȟȘȜșȎȜȝȖȟȎțȜȑȜ țȎȐȘȜșȜȠȞȖȘȡȠțȖȘȎ ABC S=– a ha S = – b c VLQĴ 2 2 b a2 + b2 = c2 ȠȓȜȞȓȚȎǽȳȢȎȑȜȞȎ Ĵ + ȕ + Ȗ = 180Ȝ d2 h a a a S = ab sinȖ 1 S=– dd , 2 1 2 a+b S=— 2 h, d1, d2 ²ȒȳȎȑȜțȎșȳȞȜȚȏȎ aȳb ²ȜȟțȜȐȖȠȞȎȝȓȤȳȴ S = ab S = aha M(x0, y0) L = 2ʌR ǸȞȡȑ ȀȞȖȘȡȠțȖȘȖ C ǽȞȭȚȜȘȡȠțȖȗȠȞȖȘȡȠțȖȘ (x – x0)2 + (y – y0)2 = R2 R ǽȞȭȚȎ ȝȞȖȕȚȎ ǽȞȎȐȖșȪțȎ ȝȳȞȎȚȳȒȎ H H ȄȖșȳțȒȞ m R ǸȜțȡȟ 1 Sȏ = PȜȟț H P m Sȏ = – 2 Ȝȟț 1 R R R S H V=– 3 Ȝȟț ǸȡșȭȟȢȓȞȎ L H H V = SȜȟț H S = ʌR2 V = ʌR2H ʌR2H V=– 3 1 ʌR3 V=– 3 4 Sȏ = 2ʌRH Sȏ = ʌRL S = 4ʌR2 ǸȜȜȞȒȖțȎȠȖȠȎȐȓȘȠȜȞȖ M(x0, y0, z0) A(x1, y1, z1) B(x2, y2, z2) x1 + x2 x0 = — 2 y1 + y2 y0 = — 2 AB (x2 – x1, y2 – y1, z2 – z1) ~AB~ (x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2 a(a1, a2, a3) a b = a 1 b 1 + a 2 b 2 + a 3b 3 Ǘ b(b1, b2, b3) a b = ~a~~b~FRVǗ ǸȳțȓȤȪȕȜȦȖȠȎ 24 z1 + z2 z0 = — 2