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 \(x + 2y + 1 = 0\).
9000063408
Level:
B
In the following list find the value of the parameter
\(x\) which
ensure that the following geometric series is divergent.
\[
\sum _{n=1}^{\infty }(5 - 3x)^{n}
\]
\(x = \frac{1}
{2}\)
\(x = \frac{13}
{9} \)
\(x = \frac{11}
{6} \)
\(x = \frac{5}
{3}\)
9000063802
Level:
B
We are given the sequence \(\left (an + b\right )_{n=1}^{\infty }\).
This sequence satisfies \(a_{4} - a_{1} = 6\). Use
this information to find \(a\).
\(a = 2\)
\(a = -2\)
\(a = -1\)
\(a = 1\)
9000063301
Level:
B
Differentiate the following function.
\[
f(x)=\sin (2x^{2} + 1)
\]
\(f'(x) = 4x\cos (2x^{2} + 1),\ x\in \mathbb{R}\)
\(f'(x) = 4x\cos x,\ x\in \mathbb{R}\)
\(f'(x) =\cos (4x),\ x\in \mathbb{R}\)
\(f'(x) =\sin (4x + 1),\ x\in \mathbb{R}\)
9000063409
Level:
B
Solve the following equation.
\[
1 + 2x + 4x^{2} + 8x^{3}+\cdots = 3
\]
\(x = \frac{1}
{3}\)
\(x = \frac{1}
{5}\)
\(x = \frac{1}
{2}\)
\(x = \frac{3}
{4}\)
9000063602
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }(-1)^{n} \frac{3}
{2n + 1}
\]
\(0\)
\(-\frac{3}
{2}\)
\(\frac{3}
{2}\)
\(- 1\)
9000063604
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\sin 2\pi n
\]
\(0\)
\(1\)
\(- 1\)
\(\infty \)
9000063605
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\log 3^{n}
\]
\(\infty \)
\(- 1\)
\(0\)
\(3\)