2010005603
Level:
A
Rationalize the denominator of \( \frac1{\sqrt[3]5} \).
\( \frac{\sqrt[3]{25}}{5} \)
\( \frac15 \)
\( \frac{\sqrt[3]{5}}{5} \)
\( \frac{\sqrt5}5 \)
A
2010005602
Level:
A
Rationalize the denominator of \( \frac{\sqrt{3}-3}{\sqrt 3} \).
\(1- \sqrt 3 \)
\( -3 \)
\( 1+\sqrt3 \)
\( 1-\sqrt3\)
2010005601
Level:
A
The mean distance of Uranus from the Sun is \( 4.53\cdot10^{12}\,\mathrm{m} \), and the mean distance of Mercury from the Sun is \( 5.79\cdot10^{10}\,\mathrm{m} \). How many times farther Uranus from the Sun than Mercury is?
about \( 78 \) times
about \( 780 \) times
\( 130\) times
about \( 8\) times
2010005402
Level:
A
Find the limit.
\[
\lim\limits_{n\rightarrow\infty}\left( \frac7{n^2} +3+\frac{7-4n^2}{3+n^2}\right)
\]
\( -1 \)
\( 0 \)
\( \infty \)
\( -\infty \)
\(1 \)
2010005401
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\left ( \frac{n+1}
{n - 1} + \frac{n -1}
{n + 1}\right )
\]
\(2\)
\(-1\)
\(0\)
\(1\)
2110005205
Level:
A
Choose the graph of a function \( f \) for which \( f'(-1) > 0 \), \( f'(0)=0 \), \( f'(2) = 0 \), \( f'(3) < 0 \) (\( f' \) is the derivative of the function \( f \)).
2110005204
Level:
A
The figure shows the derivative of one of the functions displayed below. Choose the function.
2010005203
Level:
A
The graph of \( f \) is given in the figure. Which of the following holds? (\( f' \) is the derivative of the function \( f \).)
\( f'(0)=-2 \), \( f'(2) \) does not exist, \( f'(5)=1 \)
\( f'(0)=-2 \), \( f'(2)=0 \), \( f'(5)=1 \)
\( f'(1)=0 \), \( f'(3)=0 \), \( f'(4) \) does not exist
\( f'(1)=-1 \), \( f'(3)=0 \), \( f'(4)=0 \)
2010005202
Level:
A
Given the function \( f\colon y=\frac12 x^2-4\), determine all the values of \( x \) (\( x\in\mathbb{R} \)) for which \(|f' (x)|=1 \).
\( x_1=1 \), \( x_2 =-1 \)
\( x=1\)
\( x_1=2 \), \( x_2 =-2 \)
\( x=2\)
\( x=-1 \)
2010005201
Level:
A
Given the function \( f\colon y=2x^4-x^2+4x \), find \( f'(-1) \).
\( -2\)
\( 14 \)
\( -6 \)
\( -10 \)
\( 2 \)