C | math4u.vsb.cz

1003107601

Level:

Evaluate the following integral on \( (3;\infty) \). \[ \int\frac{5x-3}{x^2-2x-3}\mathrm{d}x \]

\( \ln\!⁡\left[(x-3)^3\cdot(x+1)^2\right]+c\text{, }c\in\mathbb{R} \)

\( \ln\!⁡\left[(x-3)^2\cdot(x+1)^3\right]+c\text{, }c\in\mathbb{R} \)

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

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

1003030903

Level:

Identify which of the following functions is bounded below.

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

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

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

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

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 \( f(x)=\left(\frac12\right)^{|x|} \).

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 \( f(x)=\left|x^3+1\right| \).

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?

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

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

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

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

1003102303

Level:

Which of the following functions is decreasing on the interval \( (-\infty;0) \)?

\( m(x)=\left|x-|x-1|\right| \)

\( h(x)=\left| x+|x-1|\right| \)

\( g(x)=\left|x-|x+1|\right| \)

\( f(x)=\left|x+|x+1|\right| \)

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 \( f \) is \( [1;\infty) \).

1103102301

Level:

Let \( f(x)=|x-|x| | \), \( x\in [-5;5] \). Choose the graph of \( f \).

1003047505

Level:

Find the following limit. \[ \lim\limits_{n\rightarrow\infty}\Bigl(\frac5{\sqrt{n}}-\frac2{3^n} +\frac{(-1)^n}{2n^2-1}-7\Bigr) \]

\( -7 \)

\( 0 \)

\( -4 \)

\( \infty \)

\( -\infty \)

« first
‹ previous
…
74
75
76
77
78
79
80
81
82
…
next ›
last »

Error | math4u.vsb.cz

The website encountered an unexpected error. Please try again later.

C

1003107601

1003030903

1003101103

1003101102

1003101101

1103102304

1003102303

1003102302

1103102301

1003047505

Events

Akce

Interests

Zajímavosti

About portal

O portálu

Error