Quiz about Математический анализ 1 ЗО (п)

Question 1

$$\lim_{x\rightarrow0}\left(1-2x\right)^{\frac{1}{x}}=$$

Accepted Answer

$$\frac{1}{e^2}$$

Answer

$$e^2$$

Answer

$$\sqrt{e}$$

Answer

$$\frac{1}{\sqrt{e\ }}$$

Question 2

$$\lim_{x\rightarrow\infty}\frac{\sin x}{x}=$$

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$\infty$$

Answer

$$-1$$

Question 3

$$\lim_{x\rightarrow2}\frac{\ln\left(3-x\right)}{x^2-4}=$$

Accepted Answer

$$\frac{1}{4}$$

Answer

$$\frac{3}{4}$$

Answer

$$0$$

Answer

$$\infty$$

Answer

$$\frac{1}{2}$$

Question 4

$$y=\frac{1}{\ln x}$$ , $$y$$

Accepted Answer

$$-\frac{1}{x\ln^2x}$$

Answer

$$-\frac{1}{x\ln x}$$

Answer

$$\ln\ln x$$

Answer

$$-\frac{1}{\ln^2x}$$

Question 5

$$y= ext{tg}^2x$$ , $$y$$

Accepted Answer

$$\frac{2 ext{tg}\ x}{\cos^2x}$$

Answer

$$\frac{2x}{\cos^2x}$$

Answer

$$\frac{1}{\cos^4x}$$

Answer

$$2 ext{tg}\ x$$

Question 6

$$\int\frac{dx}{\left(1-x\right)^3}=$$

Accepted Answer

$$\frac{1}{2\left(1-x\right)^2}+C$$

Answer

$$\frac{2}{\left(1-x\right)^2}+C$$

Answer

$$-\frac{2}{\left(1-x\right)^2}+C$$

Answer

$$-\frac{1}{2\left(1-x\right)^2}+C$$

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