1003047502
Level:
C
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}\frac 4{2\sqrt{n}-3} \]
\( 0 \)
\( 2 \)
\( \frac12 \)
\( 4 \)
\( \infty \)
C
1003047501
Level:
C
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}(2\sqrt{n}-3) \]
\( \infty \)
\( 2 \)
\( -1 \)
\( 0 \)
\( -3 \)
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 \( f(x)=\sqrt{|-x|};\ x\in [-9;9] \).
1103082705
Level:
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is false.
\( f(x)=\log_2|x|;\ x\in[0.25;8] \)
\( f(x)=|\log_2 x |;\ x\in[0.25;8] \)
\( f(x)=|-\log_2 x|;\ x\in[0.25;8] \)
\( f(x)=\left|\log_{\frac12} x \right|;\ x\in[0.25;8] \)
1103082704
Level:
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is true.
\( f(x)=2^{|x|};\ x\in[-2;2] \)
\( f(x)=\left|2^x\right|;\ x\in[-2;2] \)
\( f(x)=\left|x^2+1\right|;\ x\in[-2;2] \)
\( f(x)=\left|2^{-x}\right|;\ x\in[-2;2] \)
1103082703
Level:
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is true.
\( f(x)=-|\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|\cos x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|-\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=-0.5\cdot\sin x;\ x\in[-2\pi;2\pi] \)
1103082702
Level:
C
Function \( f \) is given completely by the graph. Identify which of the following statements is true.
\( f(x)=\left|x^2-1\right|;\ x\in[-2;2] \)
\( f(x)=\left|x^2\right|-1;\ x\in[-2;2] \)
\( f(x)=-\left|x^2+1\right|;\ x\in[-2;2] \)
\( f(x)=\left|-x^2\right|+1;\ x\in[-2;2] \)
1103082701
Level:
C
Function \( f \) is given completely by the graph. Identify which of the following statements is false.
\( f(x)=\frac1x;\ x\in[-2;-0.5] \)
\( f(x)=\left|-\frac1x\right|;\ x\in[-2;-0.5] \)
\( f(x)=\frac1{|x|} ;\ x\in[-2;-0.5] \)
\( f(x)=-\frac1x;\ x\in[-2;-0.5] \)
1103064107
Level:
C
Decide which of the following diagrams shows the solution set of the given inequality.
\[ \left(\frac13\right)^{x(x+1)} \geq\left(\frac1{27}\right)^2 \]
