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Экзамен МА-1 ЗФ-213

Authored by Oxana Sheremet

Mathematics

University

Used 5+ times

Экзамен МА-1 ЗФ-213
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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Укажите график функции y=log⁡3xy=\log_3x

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2.

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Найдите предел lim⁡x→0 tg xx\lim_{x\rightarrow0}\ \frac{\text{tg}\ x}{x}

1

0

∞\infty

- 1

3.

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Найдите предел lim⁡x→∞ 3x2+4x+1x2+100\lim_{x\rightarrow\infty}\frac{\ 3x^2+4x+1}{x^2+100}

33

1100\frac{1}{100}

3100\frac{3}{100}

0

∞\infty

4.

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Найдите производную функции y=2xy=2^x

y′=2xln⁡2y'=2^x\ln2

y′=2xln⁡xy'=2^x\ln x

y′=x 2x−1y'=x\ 2^{x-1}

y′=2xy'=2^x

5.

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Найдите производную функции y=ctg⁡4xy=\operatorname{ctg}4x

y′=− 4sin⁡24xy'=-\frac{\ 4}{\sin^24x}

y′=4cos⁡24xy'=\frac{4}{\cos^24x}

y′=−4 tg 4xy'=-4\text{ tg}\ 4x

y′=−1sin⁡216xy'=-\frac{1}{\sin^216x}

6.

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Найдите производную функции y= 1+x2y=\sqrt{\ 1+x^2}

y′=x1+x2y'=\frac{x}{\sqrt{1+x^2}}

y′=121+x2y'=\frac{1}{2\sqrt{1+x^2}}

y′=21+x2y'=\frac{2}{\sqrt{1+x^2}}

y′=2x1+x2y'=\frac{2x}{\sqrt{1+x^2}}

7.

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Найдите интеграл ∫ dxx3\int\ \frac{dx}{x^3}

−12x2-\frac{1}{2x^2}

−4x4-\frac{4}{x^4}

−2x2-\frac{2}{x^2}

−14x4-\frac{1}{4x^4}

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