Algebra misollar

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Questions and Answers

Agar A(0;0;1) , B(3;2;1) , C (4;6;5) , D(1;6;3) berilgan bo‘lsa, a = AB + CD vektorni toping.

a = (0;2;-2) (correct)
a = (5;14;10)
a = (7;1;0)
a = (4;7;-2)

A(6;4;2) va B(8;-2;5) berilgan bo‘lsa, AB vektorning uzunligini toping.

5
3
7 (correct)
6

Agar a = 2, b = 3, $\widehat{a \cdot b} = 60^\circ$ bo‘lsa, a × b skalyar ko‘patma nimaga teng?

2
3 (correct)
6
4

A = (2;3;-1) va b = (1;-5; m) vektorlar m-ning qanday qiymat-larida o‘zaro perpendikulyar bo‘ladi?

13 (A) Signup and view all the answers

A = 2i - j va b = 3k vektorlar berilgan. a × b vektorli ko‘paytma topilsin.

<ul> <li>3i + 6 j (A)</li> </ul> Signup and view all the answers

A = ( x1 ; y1 ; z1 ) , b = ( x2 ; y 2 ; z 2 ) , c = ( x3 ; y3 ; z3 ) vektorlarning komplanarlik sharti qanday?

$\begin{vmatrix} x_1 & y_1 & z_1 \ x_2 & y_2 & z_2 \ x_3 & y_3 & z_3 \end{vmatrix} = 0$ (C) Signup and view all the answers

Ordinata o‘qidagi b = -3 nuqtadan o‘tuvchi va Ox o‘qining musbat yo‘nalishi bilan $\alpha = \frac{\pi}{6}$ burchak tashkil qiluvchi to‘g‘ri chiziq tenglamasini ko‘rsating.

$x - \sqrt{3}y - 3\sqrt{3} = 0$ (A) Signup and view all the answers

A(3;-1) va B ( 4;2) nuqtalar orqali o‘tuvchi to‘g‘ri chiziq tenglamasi tuzilsin.

y = 3x - 10 (B) Signup and view all the answers

$y = \arcsin e^x$ funksiyaning hosilasi topilsin:

$y' = \frac{e^x}{\sqrt{1 - e^{2x}}}$ (A) Signup and view all the answers

$x^2 + y^2 = 1$ oshkormas funksiyaning hosilasi topilsin:

$y' = -\frac{x}{y}$ (C) Signup and view all the answers

$y = \arccos(1-2x)$ funksiya hosilasini toping

$y' = \frac{1}{\sqrt{1 - 4x^2}}$ (C) Signup and view all the answers

$y = x - \arctan x$ funksiya hosilasini toping

$y' = \frac{1}{1+x^2}$ (A) Signup and view all the answers

$y = 4x - x^2$ funksiyaning ekstremumini hisoblang

x=2, $y_{max}$=4 (D) Signup and view all the answers

$y = \sqrt{x}$ funksiyaning o‘sish oraliqini toping

x>0 (B) Signup and view all the answers

$y=x+2\sqrt{x}$ funksiya hosilasini toping

$1 + \frac{1}{\sqrt{x}}$ (C) Signup and view all the answers

$x^2 + y^2 + x = 0$ aylananing radiusini toping.

$\frac{1}{2}$ (C) Signup and view all the answers

$y = 3^x$ funksiyaning hosilasini toping.

$3 \cdot \ln 3$ (D) Signup and view all the answers

$y = 3x - x^3$ funksiyaning monoton o'suvchi oralig'ini toping.

$- 1 \le x \le 1$ (B) Signup and view all the answers

$$\lim_{n \to \infty} \frac{n^3 - 100n^2 + 1}{100n^3 + 15n}$ ni hisoblang.

$\frac{1}{100}$ (A) Signup and view all the answers

$$\lim_{n \to \infty} \frac{2n - 1}{2n + 1}$ ni hisoblang.

$1$ (C) Signup and view all the answers

Funksiyaning aniqlanish sohasini toping: $f(x) = \frac{x-2}{x^2 -1}$

$( - \infty; - 1) \cup (- 1; 1) \cup (1; \infty)$ (D) Signup and view all the answers

Funksiyaning aniqlanish sohasini toping: $y = \arccos \frac{3x + 4}{5}$

$[-3;1/3]$ (B) Signup and view all the answers

Funksiyalardan qaysi biri toq funksiya?

$y = \sin^3 x - 7x$ (B) Signup and view all the answers

Funksiyaning uzilish nuqtalarini toping: $y = \frac{x-3}{x^3 - 9x}$

$0; -3; 3$ (A) Signup and view all the answers

$\lim_{x o -1} (x + 1)$ ni aniqlang.

0 (C) Signup and view all the answers

$\lim_{n o \infty} \dfrac{n^3 + 4n^2}{2n^3 + n^2 - n + 1}$ ni aniqlang.

1/2 (D) Signup and view all the answers

Agar $y = \frac{10}{x^3}$ bo'lsa, $\frac{dy}{dx}$ ni toping.

$-\frac{30}{x^4}$ (C) Signup and view all the answers

Agar $y = \sin(6x)$ bo'lsa, $\frac{dy}{dx}$ ni toping.

$6\cos(6x)$ (B) Signup and view all the answers

Agar $y = x^2 \cos(x)$ bo'lsa, $\frac{dy}{dx}$ ni toping.

$x(2\cos(x) - x\sin(x))$ (C) Signup and view all the answers

$D = \begin{vmatrix} 0 & 5 & 4 \ 9 & 6 & 3 \ 3 & 2 & 1 \end{vmatrix}$ ni hisoblang.

0 (B) Signup and view all the answers

$D = \begin{vmatrix} 4 & 2 & 1 \ 0 & 5 & 4 \ 1 & 6 & -3 \end{vmatrix}$ determinantidagi $a_{21}$ elementining $M_{21}$ minorini toping.

-12 (C) Signup and view all the answers

Agar toʻgʻri chiziq va tekislik parallel boʻlsa, $ \frac{x - 2}{3} = \frac{y + 1}{2} = \frac{z - 5}{-1} $ va $Ax + 2y + 7z + 5 = 0$ bo'lsa, A ning qiymati qanday bo'ladi?

1 (C) Signup and view all the answers

$ \frac{x^2}{20} + \frac{y^2}{16} = 1 $ ellipsning M(0;4) nuqtasidan o‘tuvchi urinmaning tenglamasini toping.

y=4 (A) Signup and view all the answers

$25x^2 + 125y^2 = 625$ ellips o‘qlari uzunliklarini toping.

$a = 5, b = \sqrt{5}$ (C) Signup and view all the answers

$4x^2 - 9y^2 = 36$ giperbolaning yarim o'qlari uzunliklarini toping.

a = 3, b = 2 (B) Signup and view all the answers

Fokuslari orasidagi masofa $2c=8$, uchlari orasidagi masofa $2a=6$ bo‘lgan giperbola tenglamasini tuzing.

$ \frac{x^2}{6} - \frac{y^2}{4} = 1$ (C) Signup and view all the answers

$y^2 = 8x$ parabola direktrisasi tenglamasini tuzing.

x=-2 (B) Signup and view all the answers

Fokusi (6;0) nuqtada bo‘lgan parabola tenglamasini tuzing.

$y^2 = 24x$ (A) Signup and view all the answers

$x^2 + y^2 - 6x = 0$ aylananing radiusini aniqlang.

R = 3 (B) Signup and view all the answers

Quyidagi determinantning $a_{11}$ elementining algebraik to‘ldiruvchisini toping:

$\begin{vmatrix} a_{11} & a_{12} \ a_{21} & a_{22} \end{vmatrix}$

$a_{22}$ (A) Signup and view all the answers

Agar $\begin{vmatrix} 1 & 2 \ 3 & x \end{vmatrix} = 0$ bo‘lsa, x ning qiymatini toping.

6 (B) Signup and view all the answers

Agar $\begin{vmatrix} 4 & 2 \ -3 & 1 \end{vmatrix} = k \begin{vmatrix} -8 & 2 \ 6 & 1 \end{vmatrix}$ bo‘lsa, k ni toping.

-$\frac{1}{2}$ (A) Signup and view all the answers

10x = $\begin{vmatrix} 4 & 2 \ -3 & 1 \end{vmatrix}$ tenglamani yeching.

1 (B) Signup and view all the answers

Quyidagi determinantni hisoblang:

$\begin{vmatrix} a_1 & a_1 & b_1 \ a_2 & a_2 & b_2 \ a_3 & a_3 & b_3 \end{vmatrix}$

0 (A) Signup and view all the answers

$\begin{vmatrix} 2 & 4 & 0 \ 5 & -2 & 3 \ -1 & -3 & 2 \end{vmatrix}$ determinantning $a_{11}$ elementi minorini hisoblang.

-13 (C) Signup and view all the answers

D = $\begin{vmatrix} 1 & 0 & 3 \ 0 & 4 & 2 \ 2 & 1 & 5 \end{vmatrix}$ determinantning $A_{21}$ algebraik to‘ldiruvchisini hisoblang.

-3 (A) Signup and view all the answers

Agar $A = \begin{pmatrix} 2 & 3 & 0 \ 4 & 1 & 5 \end{pmatrix}$ va $B = \begin{pmatrix} 1 & 7 \ -2 & 3 \ 6 & 0 \end{pmatrix}$ matritsalar berilgan bo'lsa, A × B matritsani toping.

$\begin{pmatrix} 8 & 5 \ 45 & 18 \end{pmatrix}$ (D) Signup and view all the answers

Flashcards

Y = 3x - x^3

Bu funksiya uchinchi darajali monom sifatida ko'riladi.

Monoton o'suvchi intervallari

Funksiya monoton o'suvchi bo'lgan intervallarni topish jarayoni.