Quiz about analiz2-1

Question 1

$$\lim_{x\rightarrow\infty}\ \frac{3+2x+2x^2+3x^3}{4+5x+2x^3}=?$$

Accepted Answer

$$\frac{3}{2}$$

Answer

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

Answer

0

Answer

$$\infty$$

Question 2

$$y=2x^2+\cos\left(2x+2\right)\ \ \ \Longrightarrow\ y\ $$

Accepted Answer

4x-2sin(2x+2)

Answer

$$2x+\sin\left(2x+2\right)$$

Answer

4x+2sin(2x+2)

Answer

4x+2cos(2x+2)

Question 3

y=ln(2x+3)+arctan(2x) $$\Longrightarrow\ y\ $$

Accepted Answer

$$\frac{2}{2x+3}+\frac{2}{1+4x^2}$$

Answer

$$\frac{1}{2x+3}+\frac{1}{1+x^2}$$

Answer

$$\frac{2}{2x+3}+\frac{2x}{1+x^2}$$

Answer

$$\frac{1}{2x+3}+\frac{2x}{1+4x^2}$$

Question 4

$$\lim_{x\rightarrow\infty}\ \frac{3+2x+2x^2+3x^3}{2+3x+3x^2}=?$$

Accepted Answer

$$\infty$$

Answer

0

Answer

1

Answer

$$\frac{2}{3}$$

Question 5

$$\lim_{x\rightarrow\infty}\ \frac{3+2x+2x^2+3x^3}{2+3x^2+x^4}=?$$

Accepted Answer

0

Answer

$$\infty$$

Answer

3

Answer

$$\frac{2}{3}$$

Question 6

$$y=\arcsin\left(x^2\right)+e^{\left(x^2+3\right)}$$

Accepted Answer

$$\frac{2x}{\sqrt[]{1-x^4}}+2xe^{\left(x^2+3\right)}$$

Answer

$$\frac{2x}{\sqrt[]{1-4x^2}}+\left(2x+3\right)e^{\left(2x+3\right)}$$

Answer

$$\frac{2x}{\sqrt[]{1+2x^2}}+2xe^{\left(x^2+3\right)}$$

Answer

$$\frac{2x}{\sqrt[]{1-x^4}}+\left(2x+3\right)e^{\left(x^2+3\right)}$$

Question 7

$$y=\ln\left( an x ight)+\sec x\ \ \ \Longrightarrow\ \ y\ $$

Accepted Answer

$$\frac{\sec^2x}{ an x}+\sec x\ an x$$

Answer

$$\frac{1}{ an x}+ an^2x$$

Answer

$$\frac{\sec^2x}{ an x}+\sec^2x$$

Answer

$$\frac{1}{\sec^2x}+ an^2x$$

Question 8

$$y=2^{\arcsin x}\ \ \ \Longrightarrow\ y\ $$

Accepted Answer

$$\frac{\ln2}{\sqrt[]{1-x^2}}2^{\arcsin x}$$

Answer

$$\frac{1}{1+x^2}2^{\arcsin x}$$

Answer

$$\frac{1}{\sqrt[]{1-x^2}}2^{\arcsin x}$$

Answer

$$\frac{\ln2}{1+x^2}2^{\arcsin x}$$

Question 9

$$y=x\sin\left(\cos x\right)\ \ \Longrightarrow\ \ y\ $$

Accepted Answer

$$\sin\left(\cos x\right)-x\sin x\cos\left(\cos x\right)$$

Answer

$$\sin\left(\cos x\right)-\cos\left(\sin x\right)$$

Answer

$$\cos\left(\cos x\right)$$

Answer

$$1+\sin x\cos\left(\cos x\right)$$

Question 10

$$y=\operatorname{arccot}\sqrt[]{x}\ \ \ \Longrightarrow\ y\ $$

Accepted Answer

$$\frac{-1}{2\ \sqrt[]{x}\left(1+x^{ }\right)}$$

Answer

$$\frac{1}{2\ \sqrt[]{x}\left(1+x^2\right)}$$

Answer

$$\frac{-1}{\sqrt[]{x}\left(1+x^2\right)}$$

Answer

$$\frac{1}{\sqrt[]{x}\left(1+x^{ }\right)}$$

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