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Экзамен МА-1 ЗФ (1)

Authored by Oxana Sheremet

Mathematics

University

Used 4+ times

Экзамен МА-1 ЗФ (1)
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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Укажите область определения функции y=ln⁡(4−x2)y=\ln\left(4-x^2\right)

(−2;2)\left(-2;2\right)

(−∞;2)\left(-\infty;2\right)

(2;+∞)\left(2;+\infty\right)

(−4;4)\left(-4;4\right)

(−∞;4)\left(-\infty;4\right)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Найдите предел lim⁡x→+∞  x102x\lim_{x\rightarrow+\infty}\ \frac{\ x^{10}}{2^x}

∞\infty

00

55

12\frac{1}{2}

 10ln⁡2\frac{\ 10}{\ln2}

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Найдите предел lim⁡x→0  arcsin⁡3x−sin⁡xtg 2x\lim_{x\rightarrow0}\ \frac{\ \arcsin3x-\sin x}{\text{tg}\ 2x}

1

0

∞\infty

−1-1

4.

MULTIPLE CHOICE QUESTION

30 sec • 2 pts

Найдите производную функции y=ecos⁡ xy=e^{\cos\ x}

y′=−sin⁡x⋅ ecos⁡ xy'=-\sin x\cdot\ e^{\cos\ x}

y′=cos⁡x⋅ esin⁡xy'=\cos x\cdot\ e^{\sin x}

y′=sin⁡x⋅ esin⁡xy'=\sin x\cdot\ e^{\sin x}

y′=cos⁡x⋅ ecos⁡ x −1y'=\cos x\cdot\ e^{\cos\ x\ -1}

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Найдите производную функции y= sin⁡xxy=\frac{\ \sin x}{x}

y′=x⋅cos⁡x−sin⁡xx2y'=\frac{x\cdot\cos x-\sin x}{x^2}

y′= −xcos⁡x−sin⁡xx2y'=\frac{\ -x\cos x-\sin x}{x^2}

y′= xsin⁡x−cos⁡xx2y'=\frac{\ x\sin x-\cos x}{x^2}

y′=−xsin⁡x−cos⁡xx2y'=\frac{-x\sin x-\cos x}{x^2}

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

Определите по графику функции значение производной в точке x=0x=0

0

11

−1-1

не существует

7.

MULTIPLE CHOICE QUESTION

1 min • 2 pts

Найдите интеграл ∫ xe2x2dx\int\ xe^{2x^2}dx

12e2x2\frac{1}{2}e^{2x^2}

14e2x2\frac{1}{4}e^{2x^2}

 x22e2x2\frac{\ x^2}{2}e^{2x^2}

 x24e2x2\frac{\ x^2}{4}e^{2x^2}

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