1045●60;70 /
104510●40π ³
104560●10√2 20√3/3
()
105●2 | xlogx10=5x. |
105●25² ( ∆)
105●5
105●5. |10lg5|
Ordm;
105●4;5
105●2 |log10=5|
105●√2(√3+1)/4 |sin 105|
1050●1-2550,2-2450
105002●{-2;1;0}
105048●AB=5/sin48
105051●1 logx+1(x0,5)=logx0,5(x+1)
105051●1/3
105070●1/8 {sin10ºsin50ºsin70º
1051●1 | f(x)=1/x. f(0,5)f(1) |
105122950●3.
105123975●3
10515●1/4 |sin105sin15=?|
1051515165225●2.
105195135●√2/2.
1052●2 1/2; 2 ()=+1/ [0,5; 2]
1052●9 x10,5<2
1052●9
1052●4%
1052●12
1052●[0,5; 1,5] (y=10,5sin2x)
105218●3 /.
1052562●n=10.
Ordm; ( )
1053●11 ( ∆)
105434●1/10
105434●1/10. |1 ∫ 0,5 (4x3)4dx|
Cm.
10570●y=2x1,4.
10575●0. |cos 105º + cos 75º|
10575●2sin 15º. |cos 105º cos 75º.|
7
105912●54
1060●180π
Cm.
106045●20/1+√3; 10√2/1+√3
D )
106515●27
10658●(5;8) U (13;+∞)
10662036●6
1068●96π ²
( )
.
107●1/8
107●lg√3
107●0,49 |1sinαcosαtgα, cosα=0,7|
1070●12a²
1071213107313●1/3
107128●(1;0)
1072210722●396
10731213107313●1/3
107502●907,5
.
Cm ( BD)
108●8
108●96π ³ ( )
108●96π ³
108●48 ²( )
)
1080●8
10801260●0,8
1080318●0,5
108080●1
1080801070●1
11
10823●m²n³
108335●4,4
1083●119,2
10835●(1;2)
10835●3
1084●12
.
108722718●2
Ordm;
11●0 |√+1=1|
11●0 (sinx/1cosxcosx+1/sinx)
11●[1;+∞) |1>1|
11●y=1/x1 |=1+1/|
11●y=1+1/x |y=1/x1|
11●x>1 f(x)=lg(x+1)+lg(x1)
11●(∞;1)u(1;∞)
Sina
11●1/x²1 |f(x)=ln√1x/1+x|
|
|
11●1x√x (1√x)(1+√x+x)
11●1/2x²lnx+C y(x)=(√x+1/√x)(√x1/√x)
11●2 (logm 1/m+log 1/m)
11●4; 5
11●(1/2;1) |/1>1|
11●3π/2. |arccos(1)arcsin(1).|
11●2/cosx |cosx/1sinx+cosx/1+sinx|
11●2 |(1+sinxcosx)(sinx1cosx)/sinxcosx|
11●(∞;1)U(1/2; +∞)
Sina
11●π/2+2πn,n*Z,2πk,k*Z (cosx/1sinx=1+sinx)
11●π/4+πn<x<π/2+πn,n*Z |sinx>1 tgx>1|
11●π+2πn,n*Z |y=sinx1/cosx+1|
11●(0;1)
11●(∞;0)U(2;+∞)
11●(∞;0]
11●(-∞;-1)U(-1:∞)
11●(∞;1)U[1;+∞) |=√1/+1|
11●[1;+∞) |√1>1|
11●[0;1] {||+|-1|≤1
11●[0;1] {||+|1|=1
11●0 |√+1=1|
11●1/1-²
11●1/cos α
11●1/sin |1/tg+sin/1+cos|
11●1/sinα |1/tgα+sinα/1+cosα|
11●1/²1 {f(x)=ln√1-x/1+x
11●2/(1)² (f(x)=ex+1/ex1)
11●2/3x√x+2√x+x²/x+lnx+C |f(x)=√x+1/√x+x+1/x|
11●2/sinα |sinα/1+cosα+sinα/1cosα|
Cos2y
11●sin²x { (1cosx)(1+cosx)
11●cos²x { (1sinx)(1+sinx).
11●sin²α { (osα1)(1+cosα)
11●tg θ/2 |1+sinθcosθ/1+sinθ+cosθ|
11●cos² α
11●2tg α |cosα/1sinαcosα/1+sinα|
11●ln(x+1)+1
11●sin2y |(cosy -1)(1+cosy)|
11●sin2 |(1-cosx) (1+cosx)|
11●sinα |(1-cosα)(1+cosα)/sinα|
11●cosα |(1sinα)(1+sinα)/cosα|
11●√5/5 {y=√x (1;1)
11●ab |a/bb/a/1/a+1/b|
11●/
11●sin²λ
11●cos²λ
11●ctg x/2 (1+sinx+cosx/1+sinxcosx)
11●f(x)=ln|x+1|+C |f(x)=1/x+1|
11●6
110●1
110●(∞;-1)U [0;1)
110●1 |=1/, =1, =, =0|
110●35º, 35º ( )
110●145º 35º ( )
110●(∞;1)U[0;1)
110021310●11
110024●100, 200, 800
.
110024●100, 200, 800
110122●3π/4.
11013●19 (bn), b1=10, bn+1=bn+3)
1102●1/x5
110205●6,3
11021231●60
Ordm;.
110233●30
110310●4
110411●50
1105●2
)
11099154●11
111●0 |√a√a+1+1/√a+√a+1|
111●0 (1/logxya1/logxa1/logy)
111●1 1/loga(abc)+1/logb(abc)+1/logc(abc)=? a,b,c*R
111●2 |1/√a+b+1/√a√b/1/√a√b√a/ab|
111●25 |{√+√=11 √√=1|
111●xy/yx.
111●(∞;2)U[1;∞) |1/+1≤1|
A
111●ab | (a1+b1/a+b)1|
N,
|
|
1110●π/2+2πn,n*Z |(1+cos x)(1/sinx1)=0|
1110●=1/2+1/2
1110●+2-1=0
111010110010011000●a>b>c
111015●2:3
1111●0 (1tgx/1+tgxctgx1/ctgx+1)
1111●a1 b1 | (1 b 1 1 b 1 a 1) |
1111●6 (n), a1=1, an+1=an+1)
1111●a-b/a+b |1/b1/a/1/b+1/a.|
1111●(a-b)(a+b)
1111●2sinα |(1+cos1α+tgα)(1cos1α+tgα)|
1111●2/sin²α |1/1+cosα+1/1cosα|
1111●4√ /1
1111●1 |1/1+tgx+1/1+ctgx=?|
1111●1
1111●y²x²/x²y²
A
1111106145●64
1111108●9/13
111111●1
111111●arctg√2
1111111●1. DA+A1B1+CC1
1111111●AC1→ (AD+D1C1+BB1)
11111111●AB→
11111111●31/
111111112●1 5/8.
11111111810●54√3cm² ( )
11111111810●5√3
111111151111130502●300
Ordm;
111111456111●2,5.
111111506●10
11111521●(4; 7)
111112311111●3
1111125●(4;3),(4;3)
11111250●(4;3)(4;3)
1111211●4
11112113151●√38
1111211151●1/3.
11112112151●1/3
Chas
1111212313●5/ (+5)
11112123134145●5/x(x+5)
)
11112311111●3√2
11113●√5;√5 |+1/1+1/+1|
11113●(∞;1)U(1;∞)
11114●[5;+∞) |√x+√x+11+√x√x+11=4|
M
11114511130●²(4+√2)
111146601145●40√3
111160145●³(4+√3)
1111614127●18/17
.
.
1112●1
1112●π/4+πn,πn, n*z
1112●0; 0; 0; 0; 0 |n=(1)n+(1)n-1/2|
1112●1.
1112●2 |1 ∫ 1(x(x+1)(x+2))dx|
1112●2 |logπ(x+1)+logπx=log 1/π 1/2|
M
11122●8. (1/11/2, =2)
111211141118111●7/16
11121312●15
11122●8 |1/11/2 =2|
111221●1x/2x1
11122132●910
111222121212●→b→
11122532124935213●33,36
111230111230●4√30
111231●2
1112340441● ө
11124133614481505625●2,32
1112421●1-/2-1
111258●4
1113●1/36.
1113●1;2;1 |x1=1, xn+1=3xn|
111315●13
11132●1;1;1 (x1=1, xn+1=32xn)
1114●12 |√1+√11=4|
11143●1/2
1114313●3/2
11153●3363
11158●2a²1
Ordm;; 2,5.
1116123●0
1111614127●18/17
1118115140519●1/3.
111817●a17=139,s17=1275
1119●Da (1>1/19)
112●1
112●(0; 1/2) |{√+1≥1 2|
112●8
112●(-∞;1)
112●(68º;68º;44º)
)
112●(∞;1) |f(x)=1(1/2)x|
112●(∞;1)U(1;1)U(1;+∞) |=1/1√²|
112●1<<2. |y=1/√x1+lg(2x).|
112●15/8.
112●n=2n-1 {y1=1 d=2
112●1/2;2/4;3/8 |∑n=1 (1)n n/2|
112●tg²α |11/cos²α|
112●2/x²1
112●Q ( Q(1) X(1/2)
1120●0,5 f(x)=√1x/1+x²,f(0)
1120●1/2 |=1/√1,=2,=0|
|
|
1120●1,2
112014●4/5
112024525●180³;202²
1121●1 (a/a+11a/a²1)
1121●2,5; 2 f(x)=x+1/x x*[1/2;1]
Ordm;
11210235●b1=0,5, b11=512
112112●1/cos2α
112112112●9
1121121121●4,5
M
Y
1121221●1. |(1/1):²+1/²2+1+|
112123134..●9/10.
1121231341451561671781891910●9/10.
1121310●(x²1)5+C
1121311314●14/11
11211311411563●25
11214●2/3
112175158●1,5.
1122●2/3 |1 ∫ 1 dx/(x+2)²|
1122●8 ² ( )
P
1122●9/8π | y=1/x, y=x, x=1/2, x=2 |
11220●(0; 1/2)
11221●22/3
11221●2 2/3 |1 ∫ 1(x2)(x²1)dx|
11221134●0,001
Ab
11221221●3
11221314●0,001.
11221314●{10,104}
11222●tg²α. |1+(1/tg²((π/2+a)sin²α|
11222●3 |(;), {√+1=1, +2=22, /|
112220131420●0,4.
112220131420●{0,002; 200}
C
1122213...●0,4
11222321093252233210911122●2
)
112231●(1; 2; 3)
1122321122●4
11223312641122●0.
X1;y1),(x;y2)
{³√x+³√y=1 ³√xy=2, 1212
1122331321212●0
11223422201212●40
11223478●3.
112234829●5,75
1122348291122●5,75
112242220●13.
11228●20√2
2,2. ( , )
1123●4
1123●√2(1+√2√3)/4 |1/1+√2+√3|
1123●2+√2√6/4 |1/1+√2+√3|
.
1123●(8;6) (1|+1|/2>3)
112311●11
112311322●(∞;1/5)
11232143●101
11232143●120{a11=23, a21=43
11232523●0
112330●20
11233723●q=5, b3=300; q=6, b3=432
11228●20√2
112330●20
11233478●3
11233723●q=5, b3=300; / q=6, b3= 432
.
11237●68º; 37º; 75º
11238●37º;68º;75º
1124●8 (b1=1, q=2, b4?)
11242●π/2+2πn,n*Z
1124125210●1.
11245●0
1125●4-3+7=0
112610●20 2/3
1127178251011112322935126212●94,96
11283●7 |√11=28/3|
1275315835●10,4
113●(0:1)
113●(0;3] |1/x≥1/3.|
113●(∞;3) |x≤11/x3|
113●0 ( y)
113●1
113●19 (a1=1,d=3)
113021●arccos √55/55
1130273130151500013●1,36.
1131090●5
11311●(-∞;1)U(1;∞)
11311126●3
11312●1/6
1131215●1
1131231213121●1/6
113123131●0
11313●(∞;5)U(1;∞)
1131311●1.
11313131231●³√x+1
113135157●S=1/2(11/2n+1)
113114115116●√3/3
1132●√m-√n/m
|
|
1132●0 |limx→1 1+³√x/2+x|
1132015152441142518●9/20.
11322●3;5
113227●[1; 2] |1≤(1/3)2≤27|
X
11323234●5
113235●0 |1 ∫ 1/3 (23x)5dx|
113254●4 |1 ∫ 1(3x²+5x4)dx|
11327150●69.
113312●48
11331323362●19
113323●2
113343807●1,35.
113412●13
11342●2√x+13
11345214●2,9
1135●4624
1135135●4624
11356●63,28/
X
11356●x<1,5
1136251415171●55/17.
11364●2 (:1 1/3=6:4)
( )
1137110215●2 2/3
1138●36.
11380●(11;3)U(8;∞) |(+11)(+3)(8)>0|
114●2 |=1/√, , =1, =4|
114●√2; √2
1141●1/5
11423●21,3/5
114115116117118119●2 1/2
11412324354●3.
11426●a³
1143●(x+4)²+(y-3)²=25
114310125..●0,7.
114310125231●0,7.
11432253456103●2,975
X5
1147●58.
( )
115●6/25
115●40; 50
115●10. | 1 ∫ 1(5x)dx |
11502●2,24.
115114●6/25
11511611711120●80
115121●2/5.
115264●42/3
115264●4 2/3 |1 ∫ 1(5x²+6x4)dx.|
11532●1
11543●101º 36º
1154890●40/,50/.
11561212536●(2; 3)
115705155556902●15
; 60
116●28 ( ∆ )
1160●15
11602●15² ( )
11602●15²
1161412711●18/17.
11616551●7;0,1 |11=6; 16=5,5 1 d|
1161685●0,5 |11=6; 16=8,5|
)
116212●18,5
)
1164●2x+24x³
116515●297.
11652●0 |1∫ 1 (6x5+2x) dx|
116712●28.
11673●1792
11681114●6
116837●d=3
117●136
.
117177●7
)
117234922147●4,5.
11723492214706334212●4,1.
1173337●3/7
117559171101321704015025358137505234372028●4
1176●63 |1=17; d=6|
1177●≤7 |11≤77|
11776●1/6.
1178●10 (n=11 n78 )
118124●27
118125●99/8
11817●11=139; S17=1275
118192●2 (b1=18; g=1/9. b2)
1182635341●2,3km/chas
1183152●(1;3)
11838●3/2x |1(1/8)+(3/8)|
118813●6
11913111●1
11921122●88; 18
119711423●10
119781423●10
1201●y=2x+3
12●0 |f(x)=√x1/x, f(2)?|
12●1 |f(x)=lnx1/x |
12●1/2 e2x+C |f(x)=e2x|
12●(1;3) (|1|<2)
12●(1x)(1+x)
12●2;1
12●2; 1/2 | =(1/2)sinx |
12●1 (f(x)=lnx1/2 2)
12●8 (N 1/log2N)
12●108π ².
( )
( )
12●30 |arcsin 1/2|
12●30 |arcsin(1/2)|
12●60 |arccos(1/2)|
12●120 |arccos(1/2)|
12●π/6 |arcsin 1/2|
12●π/6 |arcsin (1/2)|
12●2π/3 |arccos (1/2)|
12●1 |x≥1,2|
12●1/2tg α 1/2 |1ctg2αtgα/tgα+ctgα|
12●144 ( ·D)
)
12●192 π/2 ³ ( )
12●9
Cm ( AM)
12●36²
12●√21 |1√2|
{ 12=36²
12●4/
12●6; 54
Sin2x
12●1/sin2x |f(x)=1/2ln ctgx|
12●2√2x+C
Ordm;
12●√3+1/ 1√3
12●√31/1+√3 |tg π/12|
12●√2/2 |1/√2|
12●1/18√2 | =√/+1 (2) |
|
|
12●25
)
12●2sin²a |1cos2α|
12●sin²α. {1+cos(πα)sin(π/2+α).
12●sin α {12sinα cosα/sinαcosα+cosα
12●1/(2cos² x)
12●x≠0;1 {y=1/x²+x
12●6/
12●7√2/4 |f(x)=(x+1)√x =2|
12●2π3.
12●(1)ⁿ+¹ π/6+πn; n*Z
12●(1)kπ/6+kπ,k*Z |sinx=1/2|
12●(∞;2)(-1;+∞)
12●(∞;2)U(2;+∞) |y=x+1/x2|
12●(2π/3+2πk;4π/3+2πk) k*Z
12●192√3sm³
12●3 tgα=1, tg(α-β)
12●30
12●36
12●1 {sin²a/ 1+cosa+cosa
12●4 {y=1+cosπ/2x
12●3. |tgβ, tgα=1, tg(αβ)=2|
12●4 |f(x)=elnx(1+ln²x) f(e)|
. ()
( )
Ordm;
Ordm;
12●sin²a
12●sinα |12sinαcosα/sinαcosα+cosα|
12●sinx|cosx| {sinx/√1+tg²x
12●√7 | .|
12●1200
12●x≠0; 1 |y=1/x²+x|
X
12●π/2+2kπ; π+2π | 1+cosx=ctg(x/2) |
12●π/2+2πn; π+2πn; nEZ
12●x2+3(b-a)x+2a2-5ab+2b2=0
12● |√+1=√+2|
12●π/6 |arcsin(1/2)|
12●2√2-+
12●π/2+2πn; 6π+2π
12●π/3+2πk≤x≤+π/3+2πn, n*Z {y=√cosx1/2
12●π/3+2πn≤x≤π/3+2πn n*Z
12●π/4+πn, π/2+2πn,2πn,n*Z |1+sin2x=cosx+sinx|
12●π/4+πn; π/2+2πn,2πn,n*Z |sinx+cosx=1+sin2x|
12●π /4+πn; nz |sinx cosx=1/2|
12●π/4+πn≤x≤arctg2+πn,n*Z |1≤tgx≤2|
12●π/4+πk≤x≤πk+arctg2 |1≤tgx≤2|
12●(π/6+2πn; 5π/6+2πn),n*Z |sinx>1/2|
12●(1)n π/6+πn; n*Z {ctgx+sinx/1+cosx=2
12●(2π/3+2πk; 4π/3+2πk), |cos<1/2|
12●(2π/3+2πk; 4π/3+2πk,k*Z |cosx>1/2|
12●2π/3+2πn,n*Z |cosx=1/2|
12●(2,5; 0)
12●(2; 1) a→{m; m+1;2}
12●(5;+∞)
12●[5; 3) |√12=|
12●(∞;+∞) 1+x<x+2
12●(∞;2]U(1;+∞)
12●[1;5) |√x1<2.|
12●0 {(cosa=1)
12●0 {f(x)=√x1/x,f(2)=?
12●0
12●1,5
12●1/2tga {1-ctga?tga / tga+ctga
12●1/3; 1/4; 1/5; 1/6 |xn=1/n+2|
12●1/sin2x (f(x)=-1/2lnctgx)
12●120 {arccos(-1/2)
12●192√3 ³
12●2 1/2
V )
12●288 π ³ ( )
12●3 |tga=1 tg(α+β)=2|
12●315
12●36√3 c²
12●4 |=1+cos/2x|
12●4 |f(x)=elnx(1+ln²x). f(e)|
12●7π/6+2kπ<x<π/6+2kπ,k*Z |sin x<1/2|
12●π/4+kπ |sinxcosx=1/2|
12●π/4+πn,n*Z |sinxcosx=1/2|
12●4√3
.
Cosx
( )
12●20; 30
Cosx
12●cos2xdx ∫(x+1)cos2xdx ∫udv=uv∫vdu
12●2√3.
12●d1+d2
12●{ln√3} |exex/ex+ex=1/2|
Sin2
12●sinα+cosα
12●√31/1+√3 | tg π/12|
k
12●4√3π/π ² ( )
12●6√3π ² ( )
12●√7
12●7√24
12●x≠1;≠0. |y=1+x/x²+x+x|
12●x≠2 |=+1/2+|
12●≠2 |=1/+2|
12●x*(3;7) f(x)=1 F(x)=|x2|
12●=1/2
12●A² | cosa, 1sin²x |
12●π/4+πn≤x≤arctg2+πn,n*Z (1≤tgx≤2)
12●<0,5>1,5 |x|+|x1|>2
12●<1; >2
12●36(√2+1)π
12●>2
(3; 7)
12●20; 30
Ү ғ ұғ:1,2ғ
120●2πn,n*Z | (1+cosx)tg x/2=0 |
120●(-∞;-2] [1;+∞)
120●[π/2+2πn;2π/3+2πn)U(4πn/3+2πn;3π/2+2πn],n*Z
|1/2<cost≤0|
120●1,2
120●16/15π ( =1², =0)
120●1 1/15π ( =1², =0)
120●4/3 |y=1x² y=0.|
120●√3h/3 ( )
120●(-D;-1)U(-1;1)U(1;∞)
120●³/6
120●π/2+πn<x<3π/2+2πn,n*Z
120●18√3²
120●1/2
120●x²√3/3