РЕШЕНИЯ ЗАДАНИЯ ДЛЯ ВЫПУСКНОГО ЭКЗАМЕНА ПО АЛГЕБРЕ И НАЧАЛАМ АНАЛИЗА 11-класс 11-задание

11-nji iş. Çep tarap.
Aňlatmany ýönekeýleşdiriň:
2-a-5a+2:54-a2-1= 4-a2-52+a : 5-4-a24-a2 =
= 4-a2-52+a : 2+a ●2-a-(4-a2-5) = - 2-a ;
Deňlemeler sistemasyny çözüň:
2x2-3xy=-4,3x+y=5. ; 2x2-3x5-3x+4=0; 11x2-15x+4=0; 11(x-1)(x- 411)=0; x1=1; x2= 411;
Y1=5-3x1=5-3=2; Y2= 5-3x2= 5- 3●411 = 5- 1211 = 4311 = 31011 ;
Jogaby: (1; 2) ; (411 ; 31011 ) ;
Deňsizligi çözüň:
log3x>log93x+14x ; x>0 , x>0; 3x+1 4xlog3x>log33x+14x ; x>3x+14x ; x2 > 3x+1 4x ; 4x3-3x-1>0;
(x-1)(2x+1)2>0; x≠ - 12 ; x > 1; x>0;x>1; => x € (1 ; +∞);
Jogaby: x € (1 ; +∞);
4. 120-den uly bolan jemi almak üçin 1-den başlap yzygiderli gelýän näçe sany natural sany goşmaly?
S>120; S=1+2+…+n= (1+n)●n2 >120; n2+n-240>0;
n € (-∞ ; -16)∪(15 ; +∞); n=N, n=16; Jogaby: 16.
5. Toždestwony subut ediň:
1+sin2α2=sinα+π4, 0<α<π2. 1+sin2α2 = sin2α+cos2α+2sinα·cosα2 = sinα+cosα2 =
= 12(sinα+sin(π2-α) = 12 ·2sinα+π2-α2 · cosα-π2+α2== 2sinπ4 · cos(α-π2)= 2 ·22cos(π4- α)= cos(π4- α)=
=cos(π2-(α +π4))= sin( α+π4); Subut edildi.
6. Berlen çyzyklar bilen çäklenen figuranyň meýdanyny hasaplaň:
324231085090
4000020000
y = 4x – x2 , y = 0.
S= 04(4x-x2)dx= (2x2- x33 )|40 =
= 2·16 - 643 = 96-643 = 323 = 1023 ;
Jogaby: 1023 kw. birlik,
7. Funksiýanyň grafigi abssissa oky bilen haýsy burç astynda kesişýär:
y=1x-1 ? ; y=1x-1; y=0; 1x-1=0; x=1; M0(1,0);
yˊ(x) = - 1x2 ; tg⍺ = yˊ(1) = - 112 = - 1; ⍺ = 3π4 ;
Jogaby: ⍺ = 3π4 ;

11-nji iş. Sag tarap.
Aňlatmany ýönekeýleşdiriň:
1C2-1-3:3C-1-11+C=1-3C2-1C2-1 : 3C2-1 -1 1+c =
= 1-3C2-1c+1· c+1 · c+1 -(1-3C2-1) = - 1 c-1 ; Jogaby: - 1 c-1 ; 2.Deňlemeler sistemasyny çözüň:
15x2-2xy=5,2x-y=3. 15x2-2x(2x-3)-5 =0 ; 11x2+6x-5 = 0 ;
11(x+1)(x - 511) = 0; x1= -1; x2= 511 ; y1 =2x1-3 = -2-3 = -5;
y2 =2x2-3 = 1011 -3 = - 2311 = -2111 ;
Jogaby: (-1; -5) ; (511; -2111 ) ;

3.Deňsizligi çözüň:
log2x>log43x-2x ; x>0 ;3x-2x>0 ; log2x > log23x-2x ; x > 3x-2x ;
X3-3x+2 > 0 ; (x-1)2(x+2)>0 ; x ≠ 1 ; (x-1)2>0; x+2 > 0;
x> 23 ;x ≠ 1 ;x+2 > 0 ; => x € ( 23 ;1)∪1 ; +∞ ;
Jogaby: x € ( 23 ;1)∪1 ; +∞ ;4. 200-den uly bolan jemi almak üçin 2-den başlap yzygiderli gelýän näçe sany jübüt sany goşmaly?
S>200 ; 2+4+…+2k=2+2k·k2 = k2+k>200 ; k2+k-200>0 ;
K1= -1-8012 ≈ -29,32 = -14,65 ; K2= -1+8012 ≈ -27,32 = 13,65 ;
K € (-∞;-14,65)∪13,65 ;+∞; k € N, k=14 ;
Jogaby: 14 sany jübit sany goşma;y.
5. Toždestwony subut ediň:
1-sin2α2=sinα-π4, π4<α<π2. Subudy: 1-sin2α2= cos2⍺+sin2⍺-2sinαcos⍺2= sinα-cos⍺2 =
= 12(sinα-sinπ2- α) = 12·2·sinα-π2+α2 · cosα+π2-α2 =
= 2 sinα-π4·cosπ4= sinα-π4 ; Subut edildi.
6. Berlen çyzyklar bilen çäklenen figuranyň meýdanyny hasaplaň:
y = x – x2, y = 0.
3783259123190
y=x-x2

y=x-x2
S=01(x-x2)dx = ( x22 - x32 )|10 =
= 12 - 13 = 16 ;

Jogaby: S= 16 kw. Birlik.7. Funksiýanyň grafigi abssissa oky bilen haýsy burç astynda kesişýär:
y=1-1x? y=- 1x ; y= 0 ; 1 - 1x =0 ; x=1 ; yˊ=1x2 ;
tg⍺ = yˊ(1) = 112 = 1 ; ⍺ = π4 ; Jogaby: ⍺ = π4 ;