1003102303
Level:
C
Which of the following functions is decreasing on the interval \( (-\infty,0) \)?
\( m(x)=\left|x-|x-1|\right| \)
\( h(x)=\left| x+|x-1|\right| \)
\( g(x)=\left|x-|x+1|\right| \)
\( f(x)=\left|x+|x+1|\right| \)
C
1003102302
Level:
C
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:
C
Let \( f(x)=|x-|x| | \), \( x\in [-5;5] \). Choose the graph of \( f \).
1003047505
Level:
C
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}\Bigl(\frac5{\sqrt{n}}-\frac2{3^n} +\frac{(-1)^n}{2n^2-1}-7\Bigr) \]
\( -7 \)
\( 0 \)
\( -4 \)
\( \infty \)
\( -\infty \)
1003047502
Level:
C
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}\frac 4{2\sqrt{n}-3} \]
\( 0 \)
\( 2 \)
\( \frac12 \)
\( 4 \)
\( \infty \)
1003047501
Level:
C
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}(2\sqrt{n}-3) \]
\( \infty \)
\( 2 \)
\( -1 \)
\( 0 \)
\( -3 \)
1103076811
Level:
C
A circle is inscribed into an isosceles triangle. The base of the triangle is \( 4\,\mathrm{cm} \) long and the length of the altitude to the base is \( 10\,\mathrm{cm} \). Calculate the radius of the circle.
\( 1.64\,\mathrm{cm} \)
\( 0.82\,\mathrm{cm} \)
\( 0.20\,\mathrm{cm} \)
\( 0.12\,\mathrm{cm} \)
1103076809
Level:
C
The diagram shows a square inscribed into an equilateral triangle with the side \( 4\,\mathrm{cm} \) long. Calculate the length of the side of the square. Round the result to two decimal places.
\( 1.86\,\mathrm{cm} \)
\( 2.14\,\mathrm{cm} \)
\( 3.12\,\mathrm{cm} \)
\( 4.61\,\mathrm{cm} \)
1003029303
Level:
C
The probability of a man hitting a target is \( 0{.}9 \). If the man shoots three times, what is the probability that he hits the target at least once? Round the result to three decimal places.
\( 0{.}999 \)
\( 0{.}729 \)
\( 0{.}027 \)
\( 0{.}243 \)
1103082706
Level:
C
Identify the graph of the function \( f(x)=\sqrt{|-x|};\ x\in [-9;9] \).
