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Ñeà cöông oân taäp moân Toaùn khoái 11 -Naêm hoïc 2005-2006 ÑEÀ CÖÔNG OÂN TAÄP GIAÛI TÍCH KHOÁI 11 I , CAÁP SOÁ : 1) Cho CSC goàm 2006 soá haïng, bieát u3 = 5 , u 7 = -23 .Tính u1 , d , u2006 vaø S2006 2) Cho 10 , 7 ; 4 ; … ; -77 . CSC naøy coù bao nhieâu soá haïng , tính toång caùc soá haïng cuûa CSC . 3) cho CSC bieát 2u2 u5 3 u3 3u6 2 Tìm u1 , d , S15 4) Xaùc ñònh soá haïng ñaàu tieân vaø coâng boäi cuûa moät CSN , bieát a) u5 = 96 , u6 =192 b) u4 u2 72 u5 u3 144 5) Xaùc ñònh moät CSN goàm 6 soá haïng , bieát toång 3 soá haïng ñaàu baèng 168 vaø toång 3 soá haïng cuoái baèng 21 6) Cho 3;9;27;.... Tính u8 , S8 II. GIÔÙI HAÏN HAØM SOÁ : Tìm caùc giôùi haïn sau: 1) limx2 x3x 2 2 2) lim x 2 x 6 3x 10 3) lim3x3 x 1 5x2 2 4x 3 3 4) lim x 2 8 x3 6x2 11x 6 x2 x 1 x2 3x 2 x3 5x2 3x 9 x 3 x4 8x2 9 7) lim xx4 36x2 27 x 3 8) lim x3 x 3x1 2 9) 3 lim x 3 3x2 2x 6 x2 9 10) lim x 3 x 1 2 x2 9 11) lim 2 x 0 x 2 x x 12) lim2 x 1 3x 1 x2 1 13) lim x4x x 2 1 3 14) lim 3 x 1 15) lim x 1 3 x 2 x 1 3 16) (3 2x)(x3 1) x (x 1) x2 1 17) (3 2x)(x3 1) x (x2 1) x2 1 18) x4 x2 1) x (x 1)2 4x 1 19) lim(3 x 2x)20(x 1)30 (2x 1)50 20) lim 2x2 x x 1) 4x 1 21) lim3x3 x x2 1) 3x 6 22) 2 lim x3 x 1) 4x 6 23) lim x x2 1 x 3x 5 24) lim x x 2 1 x 1 x 25) lim x 1 x x 26) lim x3 x2 x x 27) lim x2 2x 1 x2 6x 3 x III.HAØM SOÁ MUÕ­HAØM SOÁ LOGARIT Baøi 1 : So saùnh : a/ a= 32000 vaø b= 23000 e/ a= log2 5 vaøb= log2 2,5ø b/ a= 3 2 1 3 vaø b= 3 1 4 5 f/ a= log13150 vaø b=log17 290 Ñeà cöông oân taäp moân Toaùn khoái 11 -Naêm hoïc 2005-2006 0.75 0.5 c/ a= 3 &b 3 g/ a 3log5 4 &b 4log5 3 d/ a=5 9 1 510 vaø b=2 h/ a log1 33 3&b 3 log1 4 32 8 Baøi 2 : Ruùt goïn bieåu thöùc : 1, A = (a-4 – b-4) : ( a-2 – b-2) 1 1 1 1 1 1 2, B = x4 y4 x2 y2 x4 y4 . 1 2 2 1 2 4 3, C = ( x 4 x 1)(x 4 x 1)(x x 1) 4, D= a3 b3 a3 a3b3 b3 5, E = x x x 11 x : x16 1 1 1 1 6, F = a6 b6 a2 b2 1 1 1 1 a3 a6b6 b3 7, G = ab 2(a 1.b2)4.(ab 1)2 a 2b(a 2.b 1)3.a 1b 8, H = loga b2 loga2 b4 (0 < a 1) 1 log3 b 9, K = (loga b logb a 1)loga b (0 < a,b 1) Baøi 3 : Tính giaù trò caùc bieåu thöùc sau : 23.2 1 5 354 10 3 :10 2 (0.25)0 2, B= 2:4 2 (3 3)3(27) 3 5 3.252 (0.7)0 (2) 2 3, C = 57 54 5 5 5 4, D = 3 4 3 4 5 5 5 5 4 4 5, E =log3 36.log 6 3 6, F = log3 6.log8 9log6 2 7, G =log3 2.log4 3.log5 4.log6 5.log7 6.log8 7 8, H = log2 1 .log25 3 2 9, I = log 2 3.log3 5.log25 2 10, K = 36log6 5 10lg2 1 3log9 36 11, M = 49log7 5 log49 3 12, N =5log6 3 log612 13, P = 3 3 9 2log5 3 14, S = 41 log2 3 3log8 5 15,T = 81log3 5 27log9 36 34log9 4 16, V =log2log3 5 (5log3 4 ) 17, X=log3 135 15 Baøi 4 : Tính : log3 5 log405 3 18, Y= log0.5 4 log2 2006 log8 2006 1, a=log3 2 .Tính : log2 3; log3 12;log12 16; log36 4 theo a 2, c = log5 3 . Tính : log25 15 theo c 3, a = log20 3 , b =log20 5 , c = log20 7 . Tính log20 44100 theo a,b,c 4, a=logx 27 ,Tính log 3 6 x theo a 5, a = lg5 , b =lg3 , Tính log30 5 theo a,b Baøi 5 : Chöùng minh : 1, loga (loga N)3 loga (loga N) 3 lg(lgN10 ) 1 lg(lgN) 1 Ñeà cöông oân taäp moân Toaùn khoái 11 -Naêm hoïc 2005-2006 3, loga c logab c 1 loga b ( 0 < a,b,c 1 ) 4, loga b.logb clogc a 1 ( 0 < a,b,c 1 ) 2 5, loga x.loga2 x 1 (loga x)2 ( 0 < a 1, x > 0 ) 6, alogb c clogb a ( 0 0 ) 7, loga d.logb d logb d.logc d logc d.loga d loga d.logb d.logc d logabc d ( 0 0 ) logb (logb a) a logb a logb a ( 0 < a,b 1) 9, log18 6 log2 6 2log18 6.log2 6 10, (loga b logb a 2)(loga b logab b)logb a 1 loga b 11, logac (bc) loga b loga c 1 loga c 12, log2 a log2 b 2 log2 a b 2 Vôùi a 1,b 1 13, Cho x,y > 0 : 9x2 + y2 = 10xy . CMR lg3x4 y 1(lgx lg y) 14, Cho a,b > 0 : a2 + b2 = 7ab . CMR logM a 3b 1(logM a logM b) 15, Cho x,y > 0 : x2 +4y2 = 4xy . CMR 2log2 (x 2y) 3 log2 x log2 y 16, Cho a,b > 0 : a2 + 4b2 = 23ab . CMR lg a 32b 1(lga lgb lg3) 17, Cho x,y > 0 : x2 +4y2 = 12xy . CMR loga (x 2y) 2loga 2 1(loga x logb y) 18 , Cho 2 < 10 , CMR : log2 log5 2 III .PHÖÔNG TRÌNH – BAÁT PHÖÔNG TRÌNH MUÕ VAØ LOGARIT Baøi 1 : Giaûi caùc phöông trình sau : 1/ 3x2 6x 8 1 2/ 23x 2 5 3/2x2 3x 2 3x 1 4/4x2 3x 5 1 x 1 2 5/ 22x 3 41 x 6/ 5 4x 12 1 3 x 25 7/ 27x 2 1 2 x 3 8/93x 3x2 5 9/5x x 8x 1 500 10/ x2 2 x2 3x 5 x2 2 x 3 11/ x 2 x2 1 x 2 2 12/ 42x 5.4x 4 0 13/2.9x 3x 3 15/9x 2.3x 1 9 0 17/32x 5 3x 2 2 19/3x 4.3 x 3 0 21/4.22x 6x 18..32x 23/64.9x 84.12x 27.16x 0 14/9x2 4x 1 3x 2 0 16/3.52x 1 2.5x 1 0,2 18/5x 24 25 20/9x 2.4x 6x 22/9x 6x 22x 1 24/3.16x 2.81x 5.36x Ñeà cöông oân taäp moân Toaùn khoái 11 -Naêm hoïc 2005-2006 25/3.4x 1 5.6x 1 2.9x 1 0 26/6.91 1 1 13.6x 6.4x 0 27/5.4x 7.10x 2.25x 0 28/ 2 3 x 2 3 x 4 3 29/ 3 3 8 x 3 3 8 x 6 30/ (7 48)x (7 48)x 14 31/ 4 15 x 4 15 x 8 32/ 7 4 3 x 3 2 3 x 2 0 33/ (5 2 6)x (5 2 6)x 10 34/ 5x 1 10x.2 x.5x 1 35/7.3x 1 5x 2 3x 4 5x 3 37/ 52x 32x 2(5x 3x ) 36/73x 9.52x 25x 9.73x 38/22x 1 32x 52x 1 2x 3x 1 5x 2 39/ 3x + x -4 = 0 40/ 1 x 3 ... - tailieumienphi.vn
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