9000078502
Level:
A
Write the following set in an interval notation.
\[
\{x\in \mathbb{R},|x|\leq 4\}
\]
\([ - 4,4] \)
\((-4,4)\)
\((-\infty ,-4] \)
\((-\infty ,-4)\)
A
9000078503
Level:
A
Write the following set in an interval notation.
\[
\{x\in \mathbb{R},|x - 3|\geq 5\}
\]
\((-\infty ,-2] \cup [ 8,\infty )\)
\((-\infty ,-8] \cup [ 2,\infty )\)
\([ 2,\infty )\)
\([ 8,\infty )\)
9000078504
Level:
A
Write the following set in an interval notation.
\[
\{x\in \mathbb{R},|x + 10| > 7\}
\]
\((-\infty ,-17)\cup (-3,\infty )\)
\((-\infty ,3)\cup (17,\infty )\)
\((-3,\infty )\)
\((17,\infty )\)
9000079101
Level:
A
Find the intervals of monotonicity for the following function.
\[
f(x)= \frac{3x + 1}
{2x - 5}
\]
Decreasing on \(\left (-\infty , \frac{5}
{2}\right )\)
and \(\left (\frac{5}
{2},\infty \right )\).
Decreasing on \(\left (-\infty , \frac{5}
{2}\right )\cup \left (\frac{5}
{2},\infty \right )\).
Decreasing on \(\left (-\infty , \frac{5}
{2}\right )\),
increasing on \(\left (\frac{5}
{2},\infty \right )\).
Increasing on \(\left (-\infty , \frac{5}
{2}\right )\),
decreasing on \(\left (\frac{5}
{2},\infty \right )\).
9000079203
Level:
A
Find all real \(x\)
for which the following expression equals zero.
\[
1 -\frac{2x + 1}
{x - 1}
\]
\(x = -2\)
\(x = -\frac{1}
{2}\)
\(x = 0\)
\(x = -1\)
9000079102
Level:
A
Find the intervals where the following function is a decreasing function.
\[
f(x) = \frac{x^{2} + 1}
{x}
\]
\([ - 1,0)\) and
\((0,1] \)
\([ - 1,1] \)
\((-\infty ,-1] \) and
\([1,\infty) \)
\([1,\infty) \)
9000079205
Level:
A
Assuming \(x\neq 0\)
and \(x\neq 2\),
simplify the following expression.
\[
\frac{x^{3} - x^{2}}
{x - 2} \cdot \frac{2 - x}
{x^{2}}
\]
\(1 - x\)
\(x - 1\)
\(x + 1\)
\(x^{2} - 1\)
9000079201
Level:
A
Evaluate
\[
\frac{-x^{2}}
{x - y} -\frac{y - x}
{x + y}
\]
at \(x = -1\),
\(y = 2\).
\(-\frac{8}
{3}\)
\(-\frac{10}
{3} \)
\(-\frac{2}
{3}\)
\(-\frac{4}
{3}\)
9000073404
Level:
A
Find the sum of the following infinite series.
\[
\sqrt{2} - 2 + \sqrt{8} - 4 + \sqrt{32} - 8+\cdots
\]
The sum does not exist.
\(\frac{\sqrt{2}}
{1+\sqrt{2}}\)
\(\frac{\sqrt{2}}
{1-\sqrt{2}}\)
\(\sqrt{2} - 2\)
9000073405
Level:
A
Find the sum of the following infinite series.
\[
\sqrt{2} - 1 + \frac{\sqrt{2}}
{2} -\frac{1}
{2} + \frac{\sqrt{2}}
{4} -\frac{1}
{4}+\cdots
\]
\(2\sqrt{2} - 2\)
\(\sqrt{2} - 1\)
\(2\sqrt{2} + 2\)
\(\infty \)