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9000087507

Level:

Assuming

x \in R

, find the quotient of two polynomials.

(- x^{3} - x^{2} + x - 1) : (x^{2} + 1)

- x - 1 + \frac{2 x}{x^{2} + 1}

- x - 1 + \frac{x}{x^{2} + 1}

x - 1 + \frac{x}{x^{2} + 1}

x - 1 + \frac{2 x}{x^{2} + 1}

9000087508

Level:

Assuming

x \in R ∖ {0, 1, 3}

, find the quotient of the polynomials.

(- 5 x^{4} + 4 x^{2} + 3 x - 4) : (x^{3} - 4 x^{2} + 3 x)

- 5 x - 20 + \frac{- 61 x^{2} + 63 x - 4}{x^{3} - 4 x^{2} + 3 x}

- 5 x - 20 + \frac{16 x^{2} + 23 x + 36}{x^{3} - 4 x^{2} + 3 x}

- 5 x - 10 + \frac{- 61 x^{2} + 63 x - 4}{x^{3} - 4 x^{2} + 3 x}

- 5 x - 10 + \frac{- 16 x^{2} + 23 x - 36}{x^{3} - 4 x^{2} + 3 x}

9000087502

Level:

Assuming

x \in R ∖ {\pm 1}

, find the quotient of the polynomials:

(- 2 x^{4} - 3 x^{2} + 3) : (x^{2} - 1)

- 2 x^{2} - 5 - \frac{2}{x^{2} - 1}

- 2 x^{2} - 5 + \frac{2}{x^{2} - 1}

2 x^{2} + 5 - \frac{2}{x^{2} - 1}

2 x^{2} + 5 + \frac{2}{x^{2} - 1}

9000081406

Level:

For

x \in R

find the correct relationship between

| x |

and

| - x |

| x | = | - x |

| x | > | - x |

| x | < | - x |

None of them. The answer depends on the particular value of

x

9000081407

Level:

For

x, y \in R

find the correct relationship between

| x - y |

and

| y - x |

| x - y | = | y - x |

| x - y | > | y - x |

| x - y | < | y - x |

None of them. The answer depends on the particular values of

x

y

9000083606

Level:

Assuming

x \neq 2

, simplify the expression

\frac{x^{2} + x - 6}{x^{3} - 8} .

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

\frac{x + 3}{x^{2} - 2 x + 4}

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

\frac{x + 3}{x^{2} - 4}

9000081409

Level:

Among expressions

1 + | x |

| 1 + x |

1 - | x |

and

| 1 - x |

on the set

x \in (- \infty; - 1)

find the expression which has smaller values than the other expressions from this list.

1 - | x |

1 + | x |

| 1 + x |

| 1 - x |

None of them.

9000079209

Level:

Evaluate the following expression at

x = 4

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

- \frac{8}{3}

\frac{31}{3}

\frac{8}{3}

6

9000079108

Level:

Find the

x

at which the function

f

has the global minimum on the interval

(- 3; 2]

f (x) = x^{3} - 3 x + 4

does not exist

x = - 3

x = - 2

x = 1

9000079109

Level:

Find the

x

at which the function

f

has the global maximum on the interval

[1; e]

f (x) = x - 2 \ln x

x = 1

x = 2

x = e

x = e - 2

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