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Новая кодовая шпаргалка по математике для ЕНТ 2013 11 страница

⇐ ПредыдущаяСтр 10 из 23Следующая ⇒

22●[–√2;√2] {y=(sinx+cosx)2

22●–2;1 2=|х2+х|

22●2x²/x–a. |a+x–a²+x²/a–x|

22●2 |√х²–2=√х|

22●2(e x/2–1/4cos2x)+C |y(x)=e x/2+sin2x|

22●2ex–1/x•ln2 |y(x)=2ex–log2x|

22●2x•(2xln2–1)/4x√x

22●[–2; 1]–{0} |f(x)=√log(2–x/x²)|

22●(x–a)(x+ay).

22●–x+a/x.

22●2см (сторона квадр)

22●х²+2ху+у²–4

22●πk,k*Z |sin2x=2sinx|

22●πk, k*Z, arctg2+πn, n*Z |tg²x=2tgx|

22●4πn≤x≤2π+4πn, n*Z |y=2+√sin x/2|

22●х=π/2+πn, n*Z | y=2x+sin2x |

22●a•b/2c (a•b/c)

22●–45^о

22●x4–y4 {(x–y)(x+y)(x²+y²)

22●4 {(a/b+b/a)²–(a/b–b/a)²

22●sin3x

22●2cos 4x |f(x)=sin2x•cos2x|

22●3/a+b

22●a+b (a²–b²)/(a–b)

22●a–b {a²–b²/a+b

22●(–∞;–4]U[0;+∞) {|x+2|≥2.

22●(–∞; 0) U (1; ∞) |х² ∫ х 2dt>0|

22●{0;2}

22●π/3+4πn≤x≤5π/3+4πn, n*Z

22●±π/4+2πn,n*Z |cosx=√2/2|

22●±π/4+2πn,n*Z |2cosx=√2|

22●±π/4+2πk,πn,n,k*Z | sin2x=√2sinx |

22●π/4+πn,n*Z |cos2x=√2(cosx–sinx)|

22●2πn; π/6+2πn/3

22●1/3 (y=x–x²,y=x²–x)

22●1+4/x²

22●45° {arcsin(√2/2)

22●–45° {arcsin(–√2/2)

22●45° {arccos(√2/2)

22●135° {arccos(–2√2)

22●4,5 {у=х2,у=2–х

22●a+b

22●х4–у4 (х–у)(х+у)(х²+у²)

22●a4+b4+6a²b²+4a³b+4ab³ |((a+b)²)²|

22●a+x/x |a²/ax–x²+x/x–a|

22●a/xy-a²

22●ax |a²x–ax²/a–x|

22●2а/b |2a–b/a•(a/2a–b+a/b)|

22●2(ex/2–1/4cos2x)+C {y(x)=ex/2+sin2x

22●1–sin x*sin2x/sin x

22●2

22●√2 |f(x)=sin2x/√2, f(x)=?|

22●√2 |y=sin2x/√2. f(π)|

22●–2;0 (–∞;–1) (–1;∞) |у=–х²–2х|

22●–2;2 б)(–∞;0),(0;∞) в)жок |у=х/2–2х нули осу кему|

22●64/15π (Объем тела у=2х, у=х²)

22●3/5 |cos2α, ctgα=–2|

22●28 (в момент время)

22●2ex–1/x•ln2 | y(x)=2ex–log2x |

22●7/3

22●4πn(π/8+α/2)sin(α/2-π/8)

Y= 2+√sinx/2●●●4πn«x«2π+4πn.n*z

22●cos α/2 {cosαcos α/2+sinαsin α/2

22●–sin x/2

22●–sin α

22●√x+√y/ √x-√y

22●x²(1-lnx)-2(1+lnx)/(x2-2)²

22●π/2+πn

22●–ab

22●x²–x²lnx–2lnx–2/(x–2)² | f(x)=xlnx/x²–2 |

22●(–1)n+1 π/4+πn; n*Z |sinx=–√2/2|

22●(1;∞) {y=log2(x2-x)+lgx

22●(a–b)(x²+x–1)

22●(a–c)(x²–x–1)

22●[–3π/4+2πn, 3π/4+2πn],n*Z (cosx≥–√2/2)

22●[–5π/4+2πn, π/4+2πn],n*Z (sinx≤√2/2)

22●1 |√2–x²=x|

22●–1 |√2–x²=–x|

22●3π/4 |arccos(–√2/2)|

22●4 {(квадрат ауданы)

22●4 (Площадь)

22●4x³ |Упр выр x•x•x•2•2 |

22●3/5

22●5/2 (log2x=logx2)

22●4πn≤x≤2π+4πn,n*Z | y=2+√sin x/2 |

22●(5π/4+2πn;–3π/4–2πn),n*Z |x+y=π/2 sinx+siny=–√2|

22●x=5π/4+2πn; у=–3π/4–2πn; N*Z

22●7/3 |y=2–|x|, y=x²|

22●4/3 |y=x², y=2x|

22●a+b/c²–d² |ad–bc/2cd(c+d)+ad+bc/2cd(c–d)|

22●(2a+b)(x–y) {2ax+bx–2ay–by.

22●–ab {ab²–a²b/a+b.

22●m²–2 {tg²α+ctg²α=m,tg²α+ctg²α

22●sin2a

22●–45

22●x²(1–lnx)–2(1+lnx)/(x²–2)² (f(x)=xlnx/x²–x)

22●–sinx/2 {f(x)=2cosx/2

22●√7

22●–π/8+πn/2,n*Z |sin2x=–cos2x|

22●2πn, π/6+2πn/3,n*Z |sin2x–cosx=sinx–cos2x|

22●x=5π/4+2πn; y=–3π/4–2πn,n*Z

22●x=5π/4+2πn

22●xmax=–2, xmin=2 (у=2/х+х/2)

22●xmin=π/2+πn,n*Z (у=2x+sin2x)

22●π/4+π

22●y=-x?x?+x2

22●x²+4xy+4y² | (х+2у)² |

22●x²+y²/x²–y² | х/х+у+у(х+у)/х²–у² |

22●a=(0; 2)

22●(a–b)(c–a)(c–b) (a–b)²(c–a)(c–a)²(a–b)

22●4a(b–c) (a+b–c)²–(a–b+c)²

22●4a²–b² |(b+2a)(2a–b)|

22●–π/8+πn/2; n*z (sin2x =–cos2x)

22●a)-2,2; b) jok c) (-∞;0)(0∞)

22●х=–1/2 мин. нyкте

22●a)x=–2 x=–2

22●a)x=–2; x=2 б)xmax=x1; xmin=x2

22●х=1; у=3. |x²–y=–2|

22●х²+4ху+4у²(х+2у)²

22●х²+2ху+у²–4 (x+y+2)(x+y–2)

22●4a•(b–c) (a+b–c)²•(a–b+c)²

22●Нет решении или ответ

22●шешими жок (sinx+sin2x=2)

22●жауабы жок (sinx+cos2x=2)

220●1; 3/2 |у=2sinx+cos2x, [0; π|

220●12 (x+y, xlgy=2 x y=20)

220●–π/4+2πn≤x≤5π/4+2πn, n*Z |2sinx+√2≥0|

220●π/2+πk, k*Z (sin2x+2)cosx=0

220●π/2+πn, ±π/6+πk,k*Z |2cosxcos2x–cosx=0|

220●(–1)кπ/6+πк,к*Z;πn, n*Z |2sin²x–sinx=0|

220●π/2+πn,n*Z (–1)k+1 π/4+πk,k*Z |sin2x+√2cosx=0|

220●π/2+πk, k*Z

220●(–1)п+1π/4+πn

220●(–1) π/6+Пk

220●π/2+πк,к*Z,2/3π(3m±1),m*Z

220●–1 f(x)=(x²–x)•cos²x f(0)|

220●–1≤х≤2 или [–1;2] |x²–x–2≤0|

220●(–2;0) |х²+2х<0.|

220●(–∞;–2]U[1;+∞) |x²+x–2≥0|

220●(–∞;0)U(1;∞) |х² ∫ х 2dt>0|

220●4,5 |у=–х²+х+2 и прямой у=0.|

220●π+2πп,n*Z |2cos(x/2)=0|

220●π+2πk |2•cos(x/2)=0|

220●±3π/4+2πn,n*Z {2cosx+√2=0

220●3/2; 1

220●π/2+2πn

220●4

220●4*1/2

220●[–π/4+πk; 5π/4+2πк],k*Z {2sinx+√2≥0

220●–3 {f(x)=2cosx–cos2x

220●–6 и -14

220●π/2+πn; ±π/3+2πk;n,k*Z |2cos²x–cosx=0|

220●–π/4+2πn≤x≤5π/4+2πn,n*Z

220●π/2+πk

220●πn, n*Z

220●πk,k*Z {sin²x–2sinx=0

220●2

220●[–4;5]

220●45,36

220●х≤–2, х≥2

220●300; 800км/ч

220●28800гусей,15600уток

220●шешуи жок

2200●а=arctan2 y=sin2x+cos2x, в точк (0;0)

2200●–2ab

22001●5 8/15π |y=x²+2, y=0, x=0, x=1|

22002●16/15π |y=x²+2x, y=0, x=0, x=–2|

22000120●√10

220002756●7000 тенге

22005●у=–14х+11.

22011●3 1/3. |y=–x²+2, y=0, x=–1,x=1|

2202●1 1/3 |y=2x–x², y=0, x=2|

2202●5*1/3

22020●(1; 10]

22021●y=1

22021●3π/2

220220●(–1; 0)

22025●(–3;4]

22024232●2

22025222●2.

2203●(–20;–12),

2203●0,35 |sin² α/2, cos=0,3|

2203●y=4x–9 |y=x²–2x в точке х0=3|

22030●28800гус,15600уток

220308400●28800гус,15600уток

220●[–4; 5] {–х+х²≤20

22011●3 1/3

2203●у=4х–9

22037●385

2204●0,7 |cos² α/2, если cosα=0,4|

22040●–m/√m²+1 |sin220°, tg40°=m?|

2204020●1/2 |2cos20°cos40–cos20°|

2205●нет решения {√х–2+√20=√5

220516●0.25;8

22052475●45. (NOD)

221●1 |x/y=y/z x²+xz+2xy=1|

221●1;–1 |2cos²α–1|

221●(–1/√2; 1/√2) |у=–2х²+1|

221●(–∞;–1/√2)U(1/√2;+∞) |y=2x²–1|

221●a=±√2 {x²+y²=1 x–y=a

221●±2π

221●любое число

221●2tgх–2√x+C | у=2/cos²x–1/√x |

221●2/(2x+1)•ln2

221●2х²–2х/(2х–1)² {f(x)=x²/2x–1. f(x)

221●(-1)ⁿ+π/6+π,n*Z; –π/4+πk,k*Z

221●–sin2a {tg2a(sin2a-1)

221●–2sin α. |2sinα–sin2α/cosα–1|

221●(–∞;–√2]U(–1;√2] {y=√2–x²/x+1

221●(–∞;∞) |у=√2х²–х+1|

221●√2

221●–4 | f(x)=2x². Найдите (–1) |

221●π+2πn

221●2π/3n,n*Z {cosx·cos2x–sinx·sin2x=1

221●1/2<х<2 | log2xx²<1 |

221●2cosa2cosa-sin2a/1-sina

221●–ctg²α

221●–cos² α |cos²α*tg²(–α)–1|

221●–sin²α {tg²α(sin²α–1)

221●кез-келген сан

221●π/4+π/2k,k*Z

221●π/4+πn/2; n*z /sin² 2x=1/

221●πn/2;n*z /cos² 2x=1/

221●–π/2+2kπ /tg(π/2+x/2)=1/

2210●(-1)k+1π/8; ±π/2k

2210●[9;+∞) |у=х²–2х+10|

2210●–1

2210●–1/10

2210●π/2+2πn;(-1)k+1π/6+πk;к;n*Z

{2sin²x–sinx–1=0

2210●π/2+πk |ctg²x/2–1=0|

2210●–π/4+πn; nЭz /tg²x+2tg x+1=0/

2210●(-∞; -1]U[1;∞)

2210●π/6; 5π/6

2210●π/4(2k+1),k*Z |2cos²x–1=0|

2210●х=–π/8+πк/2, к*Z

2210●x≠–1 (x²+2x+1>0)

22100●f(x)=–1.

22100●√2

22100●π/6; 5π/6

22100●π/6 | 2cos2x–1=0 на интер (0; π) |

22100●83/15π (Объем тела у=х²+2, х=1, х=0, у=0)

221002●(–8;6),(6;–8)

2210048●(8;6);(6;8);(–8;–6);(–6;–8).

2210060●(0;–10),(0;10),(–8;–6),(8;–6)

22101●y=–1

221012200●9см

221012450●в четвертой

221014700●2см |х²+у²–10х+14у+70=0|

221014700221014260●12см

221016●1464 см²

221018●215кг

2210232●{7π/6, π/2}

22103●y=12x–19.

221052●1;5,5

22105824●3;4

221060●1464

2211018143●215кг

2211●ab(a–b) |(a²–b²):(a-1+b-1).|

2211●1 |ен киши y=e2x–2x на интерв(–1;1)|

2211●60

2211●60° (Опр угол наклон отр к плоск)

2211●–1/3.

2211●–1/3 |f(x)=(x+2)/(2x+1), f(1)|

2211●х=2.

2211●sin²β |ctg²β(cos²β–1)+1|

2211●a+b/ab |a–2–b–2/a–1–b–1|

22111●a²–ab+b²/ab

221111●xy

2211018143●215кг.

22111111●8√2cm²

221112131●2

221121●(–3;–2),(3,1).

2211221●1/a+b

22112222●0;1

2211231122231●3x–2.

221125225●3.

221130●(–6;–5);(6;5) |{х²–у²=11 ху=30|

2211332●(9;7)

22114520●2

2212●–3. {значение 2m–M

2212●2(ln2–2); –2 y(x)=2lnx–2x [1;2]

2212●1

2212●(3,5; 1,5)

2212●[0; 2]

2212●π/8+π/4к, к*Z |sin²2x=1/2|

2212●π/8(2k+1),k*Z |cos²2x=1/2|

2212●±π/3+πn; nЭz

2212●4.

2212●π/8(2k+1)

2212●2+2/е²

2212●–sin²α |cos²α–(ctg²α+1)sin²α|

22120●–π/2+2πk,k*Z 2πn,n*Z

22121●–8/25 {f(–2), f(x)=x²–1/x²+1

221210●(–∞;0]

221210490224210●(4;1)и(3;2)

2212121●х3

221216250●(6;–8), 5√3cm

22122●1/а | х/а(x–2a)–2(1+x)/x(x–2a)+(x–2a) |

22122●2

22122●y≠1

22122●y≠1 {y=2x²–x–1/x²+x–2

22122●y≠1; y≠2 |y=2x²–x–1/x²+x–2|

22122●√2lg2

221220●πk/2

221221●(0;+∞)

22122122●4πn/3

221221822212●2

2212220099●1–√2

22122221●{0;1}

221222223100●3/2

221222223448●––––●4,5/–/–/–/→x

221223●π/2(4n+1)

221223●(–∞;–3)U(1;+∞)

221225●90%

2212284●sin8a

22123●π/2+πn,n*Z

221231●2

221232●2

2212324228212●–1/4x.

22123381●(-5/3; 7/6)

221242●8. |2(√2+1)²:4√2|

2212424●1

22125●3

2212505113●1,5.

221252522●1.5

22126●Ни при каком действительном х

2212284●sin8x

2212360●0

2213●1

2213●9/2

22132●2 {22x+1=32

2213225●(±3;±2) |{х²+у²=13 х²–у²=5|

22132321222●–√3;√3

2213253411●явл №5

221331●–2.

221331●1 |f(x)=x–2/x²–1/3x³, f(–1)|

22133123●(3;1),(1;3)

221334●(3;1)(1;3)

22134●(3;1) (1;3) |{x²+xy+y²=13 x+y=4|

221350●{2;3}

22136●(–2;–3);(2;3);(–3;–2);(3;2).

2214●–1–32/π² |f(x)=cos²x+2/x–1, x=π/4|

2214●10 см² (площ диаг сечения)

2214●0,96.

2214●–0,96 |sinα, если sin α/2–cos α/2=1,4|

2214●(–1)k+1π/24+πk/4,k*Z |sin2x•cos2x=–1/4|

2214●±π/3+2πл |2cos2x=1–4cosx|

221410490224210●(4;1) и (3;2)

2214122232●(–3/2;–1)

2214112321932●–1

221426●ни при каком действительным x.

221426●x мани жок

22142714●2

221431●x=–3

221431●–1;3 |х²–2х/х–1=4/х+4|

22144●(0;–12)

22144122●0,25

2215210●(–5;3)

22152513●2

22153●(–∞;-3]

22153●104,9km (Какпуть прош по теч 3ч,прот 4)

2215334●104,9км

22156●200тг

221563210●{–1;0}.

2215822292225●2

2216●a=±4

22161024●–2;2

2216216●8

2217●2 |√√х+21+х=√7|

2217230●–1; log23

2218●2(x–3)(x+3) {2x²–18

22180●(–3;–3)

22181●08

22181●0≤х≤√2, х>8

22182214●(–4;–1),(4;-1);(4;1),(-4;1)

22189●(–3;–3);(3;3) |{х²+у²=18 ху=9|

221915●(3;5); (5;3);(–3;–5); (–5;–3).

222●a

222●±1 |y=2x²и у=2|

222●(x–z)(y–x+z).

222●(–3;–2)U(1;2)

222●π/4+πn;n*Z; ±2π/3+2πk,k*Z

222●π/4+(4n+1),n*Z |2sinxcosx–cos²x=sin²x|

222●(a+2c)(a–b)

222●π/2+πn; π/6+πk

222●±2π/3+2πk; π/4+πn,n*Z |sinx+sin2x=cos2x+cos²x|

222●(–∞;0)U(0;+∞)

222●(–1;∞) | f(x)=log2(log2(x+2)) |

222●(a–b)(b–c)(a–c)

222●1. |2cos² α/2–cosα|

222●1 |cos2α+2sin²α|

222●a–b (а²–2аb+b²)/(a–b)

222●sin2α/2

222●2. |((√2)√2)√2|

222●2–x (x–2)²/(2–x)

222●4 |π/2 ∫ –π/2 2cos xdx|

222●2–x |(x–2)²/(2–x)|

222●2 {tg²x+ctg²x, если tgx+ctgx=2

222●1/cos²α

222●1/sin² α {cos²α+ctg²α+sin²α

222●(–3;–2]U[1;2)

222●2x |х²–у²/х+у•2х/х–у|

222●0

222●1/2cosx

222●4x/cos²(2x²–√2)

222●–4х/sin² (2x²–√2) |f(x)=ctg(2x²–√2|

222●x²cosx y=(–2+x²)sinx+2xcosx

222●π/8+πn≤x≤3π/8+πn,n*Z |2sinxcosx≥√2/2|

222●(–1)kπ/8+π/2k, k*Z |2sin2x=√2|

222●(–1)nπ/8+π/2n, n*Z |sin2x=√2/2|

222●(π/8+Пn; 3π/8+πn)

222●±π/8+πk,k*Z |cos2x=√2/2|

222●±π/6+πn,n*Z |cos2x=2sin²x|

222●1/b–а

222●cos x (f(x)=2sin x/2 cos x/2)

222●sin²x |tg²x–sin²x•tg²x|

222●1/sin2α–cos2α+ctg2α+sin2α

222●1/2 sin2α |2cos α/2 sin α/2 cosα|

222●2π {у=(sinx/2+cosx/2)2

222●2х

222●е2.

222●6 (y=2x²+x, абцисс –2)

222●х(х+1)(а+в-с)

222●(x+2y)(x²–1) |x²(x+2y)–x–2y|

222●х2cosx

222●a²+4x²+x4–4ax+2ax²–4x³

222●а={0;1} |х²–2у²=а х+у=а

222●a²+4/4a

2220●(1;2)

2220●(5;5) |{logyx+logxy=2 x²–y=20|

2220●(–1;0)

2220●2

2220●4x+10/√x

2220●πn, n*Z,–π/4+πк

2220●π/2+2πk,k*Z {2sinx–cosx–2=0

2220●–π/4+πn,n*Z |sin2x+2sin²x=0|

2220122522232●1/4

222001013●3π+π/2

22202●у=–8х+10

222022●–2ab.

22202212●(–4;–2),(–4,2)(4,–2)(4.2)

222025222●4b–2c/2b+c

22203003300040044000●a>b=c

222035015●–0,33.

22206●(4;–2);(2;–4) |{х²+у²=20 х–у=6|

2221●sin2x+1

2221●–1/2cosx+1 |f(x)=sin x/2·cos x/2,F(x),M(π/2;1)|

2221●–2/x+2cosx+x+C |f(x)=2/x²–2sinx+1|

2221●(2;1);(–2;–1) | {x²–xy=2 y²–xy=–1 |

2221●(π/2–πn; πn),n*Z

2221●1 (sin α/2+cos α/2)²/1+sin α

2221●b–a

2221●cos2α

2221●sin2x+1 |f(x)=2cos2x, F(x), M (π/2; 1)|

2221●x≥0 |x=√2x²+y²–1|

2221●x=π/4+πn/2; y=π/4–πn/2;n*Z

2221●х=2.

2221●х=2 {logx (x²–2x+2)=1

2221●a+b/a–b {(a–b)²/a²–b²)–1

2221●π/2+πk |sin²x+2cos²x=1|

2221●±π/8+kπ/2,k*Z |2•sin²2x=1|

2221●π/8+(2k+1),k*Z |2•cos²2x=1|

222100●(6;–8);(–8;6). {x+y=–2 x²+y²=100

222102●3.

2221111222210●–8

22211221●(6;9]

22211221●9

2221212222●1; 3; 4

222122522232●1/4.

222123●11

2221272●–3;1

2221312432●3/1–x

2221322●[–6;6] |x²–2√x²+13=22|

22214●6

222146●(3;2);(–3;–2).

22216●1

22216240●(–√2;–√2)U(√2;2)

2221822214●(–4;–1),(4;–1);(4;1),(–4;1)

2222●(2;5)

2222●4

2222●–xy. | x–x²–y²/x–y)•(y+x²–y²/x+y |

2222●–x–y/x+y |x/x–y+x²+y²/y²–x²+x/x+y|

2222●tg² α/2 |2sinα–sin2α/2sinα+2sinα|

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