9000064108
Level:
B
Find the normal line to the graph of the function
\(f(x) = 2x^{2} - 7x\) parallel to
the line \(y = -x\).
\(x + y + 4 = 0\)
\(- x + y + 4 = 0\)
\(x - y - 8 = 0\)
\(x + y - 8 = 0\)
B
9000064109
Level:
B
Find the tangent to the graph of the function
\(f(x) = 3x^{2} - 8x + 2\) perpendicular
to the line \(x + 4y + 5 = 0\).
\(4x - y - 10 = 0\)
\(-4x + y + 1 = 0\)
\(8x - 2y + 1 = 0\)
\(-8x + 2y - 10 = 0\)
9000064110
Level:
B
Identify a true statement related to the function
\(f(x) = \frac{x-1}
{x+1}\).
The tangent at \(T = [-3,2]\)
is parallel to \(x - 2y + 1 = 0\).
The tangent at \(T = [-3,2]\)
contains the point \(A = \left [1,-4\right ]\).
The slope of the tangent at \(T = [-3,2]\)
is \(2\).
The tangent at \(T = [-3,2]\) is
perpendicular to \(x + 2y + 1 = 0\).
9000065504
Level:
B
Evaluate the following integral on the interval \((0,+\infty)\).
\[
\int (1 -\sqrt{x})(1 + \sqrt{x})\, \mathrm{d}x
\]
\(x -\frac{1}
{2}x^{2} + c,\ c\in \mathbb{R}\)
\((x -\frac{1}
{2}x^{2})(x + \frac{1}
{2}x^{2}) + c,\ c\in \mathbb{R}\)
\(x -\frac{1}
{2}x^{\frac{1}
{2} } + c,\ c\in \mathbb{R}\)
\((x -\frac{1}
{2}x^{-\frac{1}
{2} })(x + \frac{1} {2}x^{-\frac{1}
{2} }) + c,\ c\in \mathbb{R}\)
9000065506
Level:
B
Evaluate the following integral on the interval \((0,+\infty)\).
\[
\int \frac{x^{2}}
{\sqrt{x}}\, \mathrm{d}x
\]
\(\frac{2}
{5}x^{2}\sqrt{x} + c,\ c\in \mathbb{R}\)
\(\frac{2\sqrt{x}}
{x} + c,\ c\in \mathbb{R}\)
\(\frac{2}
{5}x\sqrt{x} + c,\ c\in \mathbb{R}\)
\(\frac{\sqrt{x}}
{x} + c,\ c\in \mathbb{R}\)
9000065307
Level:
B
In the arithmetic sequence given by the first term
\(a_{1} = 4\) and the common
difference \(d = 2\)
find the sum of the first twelve terms of the sequence.
\(s_{12} = 180\)
\(s_{12} = 72\)
\(s_{12} = 120\)
\(s_{12} = 168\)
9000065308
Level:
B
For the arithmetic sequence with the first term $a_1=3$ holds $a_n=27$ and the sum of the first $n$ terms is $195$. Find $n$.
\(n = 13\)
\(n = 14\)
\(n = 15\)
\(n = 16\)
9000065310
Level:
B
For the arithmetic sequence with \(a_{4} = 11\)
and \(a_{9} = -24\)
find the sum of the first fourteen terms.
\(- 189\)
\(189\)
\(198\)
\(- 198\)
9000064806
Level:
B
The arithmetic sequence is defined by the first term
\(a_{1} = 17\) and the
fifth term \(a_{5} = 11\).
Find the term which is seven times smaller than the third term of the sequence.
\(a_{11}\)
\(a_{2}\)
\(a_{8}\)
\(a_{17}\)
\(a_{21}\)
9000065505
Level:
B
Evaluate the following integral on \(\mathbb{R}\).
\[
\int (x^{2} + 3)(x^{2} - 1)\, \mathrm{d}x
\]
\(\frac{1}
{5}x^{5} + \frac{2}
{3}x^{3} - 3x + c,\ c\in \mathbb{R}\)
\((\frac{1}
{3}x^{3} + 3x)(\frac{1}
{3}x^{3} - x) + c,\ c\in \mathbb{R}\)
\(4x^{2} + c,\ c\in \mathbb{R}\)
\(4x^{3} + 4x + c,\ c\in \mathbb{R}\)