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
...
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