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1003107601

Level:

Evaluate the following integral on

(3; \infty)

\int \frac{5 x - 3}{x^{2} - 2 x - 3} d x

\ln [(x - 3)^{3} \cdot (x + 1)^{2}] + c, c \in R

\ln [(x - 3)^{2} \cdot (x + 1)^{3}] + c, c \in R

\ln \frac{(x - 3)^{2}}{(x + 1)^{3}} + c, c \in R

\ln \frac{(x - 3)^{3}}{(x + 1)^{2}} + c, c \in R

1003030903

Level:

Identify which of the following functions is bounded below.

h (x) = \frac{2 x - 4}{x - 2}

m (x) = \frac{x^{2} - 4}{x - 2}

g (x) = \frac{4 - x^{2}}{x - 2}

f (x) = - | \frac{x^{2} - 4}{x - 2} |

1003101103

Level:

Find the true statement about the function

f (x) = \log_{2} | x |

The function

f

is even.

The function

f

has the minimum at

x = 0

The function

f

is bounded.

The function

f

is increasing.

1003101102

Level:

Find the false statement about the function

f (x) = {(\frac{1}{2})}^{| x |}

The function

f

has the minimum at

x = 0

The function

f

has the maximum at

x = 0

The function

f

is bounded.

The function

f

is even.

1003101101

Level:

Find the true statement about the function

f (x) = | x^{3} + 1 |

The function

f

has the minimum at

x = - 1

The function

f

has the minimum at

x = 0

The function

f

has the minimum at

x = 1

The function

f

has no minimum.

1103102304

Level:

Function

f

is given completely by the graph. Which of the following statements is false?

f (x) = \frac{| x |}{x}, x \in [- 5; 0) \cup (0; 5]

f (x) = | \frac{| x |}{x} |, x \in [- 5; 0) \cup (0; 5]

f (x) = 1, x \in [- 5; 0) \cup (0; 5]

f (x) = \frac{x}{x}, x \in [- 5; 0) \cup (0; 5]

1003102303

Level:

Which of the following functions is decreasing on the interval

(- \infty; 0)

m (x) = | x - | x - 1 | |

h (x) = | x + | x - 1 | |

g (x) = | x - | x + 1 | |

f (x) = | x + | x + 1 | |

1003102302

Level:

Let

f (x) = | 1 - | x | |

. Which of the following statements is true?

Function

f

has minimum at

x = - 1

Function

f

is bounded.

Function

f

is increasing on the interval

(0; \infty)

The range of

f

[1; \infty)

1103102301

Level:

Let

f (x) = | x - | x | |

x \in [- 5; 5]

. Choose the graph of

f

1003047505

Level:

Find the following limit.

lim_{n \to \infty} (\frac{5}{\sqrt{n}} - \frac{2}{3^{n}} + \frac{(- 1)^{n}}{2 n^{2} - 1} - 7)

- 7

0

- 4

\infty

- \infty

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