C

2010005303

Level: 
C
Find the limit of the following sequence. \[ {\left(\frac{(n^{2} + 4n + 4)^{n}} {n^{2n}} \right)}_{n=1}^{\infty } \] Hint: The limit of the sequence \({\left({\left(1 + \frac{2} {n}\right)}^{n}\right)}_{n=1}^{\infty }\) is \(\mathrm{e}^2\), where \(\mathrm{e}\) is the Euler number.
\(\mathrm{e}^{4}\)
\(\mathrm{e}+4\)
\(4\mathrm{e} \)
\(\infty \)

2010005302

Level: 
C
Consider the convergent sequence \[ (a_{n})_{n=1}^{\infty } = \left (\frac{6n^{2} + 10n - 300} {2n^{2}} \right )_{n=1}^{\infty } \] and its limit \(L\). Find the maximal difference between \(L\) and the subsequence \((a_{n})_{n=300}^{\infty }\). (In other words, find the maximal difference between \(L\) and the terms of the sequence starting at \(a_{300}\).)
\(0.015\)
\(0.018\)
\(0.036\)
\(3.015\)

2000006804

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequalities is it?
\[\begin{aligned} y &\leq x \\y &\geq -x \end{aligned}\]
\[\begin{aligned} y &\leq - x \\y &\geq x \end{aligned}\]
\[\begin{aligned} y &\leq x \\y &\leq -x \end{aligned}\]
\[\begin{aligned} y &\geq x \\y &\geq -x \end{aligned}\]

2000006803

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequality is it?
\[\begin{aligned} y &\leq x+2 \\y &\geq x -2 \end{aligned}\]
\[\begin{aligned} y &\leq x-2 \\y &\geq x+2 \end{aligned}\]
\[\begin{aligned} y &\leq 2x+2 \\y &\geq 2x -2 \end{aligned}\]
\[\begin{aligned} y &\leq 2x-2 \\y &\geq 2x +2 \end{aligned}\]