9000063409
Level:
B
Solve the following equation.
\[
1 + 2x + 4x^{2} + 8x^{3}+\cdots = 3
\]
\(x = \frac{1}
{3}\)
\(x = \frac{1}
{5}\)
\(x = \frac{1}
{2}\)
\(x = \frac{3}
{4}\)
B
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.
\[
\lim _{n\to \infty }\log 3^{n}
\]
\(\infty \)
\(- 1\)
\(0\)
\(3\)
9000063607
Level:
B
Find the following limit.
\[
\lim _{n\to \infty } \frac{1}
{\log 10^{n}}
\]
\(0\)
\(1\)
\(10\)
\(\infty \)
9000063608
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\frac{2^{n} + 3^{n}}
{3^{n}}
\]
\(1\)
\(2\)
\(3\)
\(\infty \)
9000063806
Level:
B
Consider the sequence \(a_{n+1} = a_{n} - 2a_{n-1}\)
with \(a_{3} = 0\)
and \(a_{4} = -16\).
Find \(a_{2} - a_{1}\).
\(4\)
\(16\)
\(- 4\)
\(8\)
9000063302
Level:
B
Differentiate the following function.
\[
f(x)= (3x^{2} + 2)^{3}
\]
\(f'(x) = 18x(3x^{2} + 2)^{2},\ x\in \mathbb{R}\)
\(f'(x) = 18x(3x^{2} + 2),\ x\in \mathbb{R}\)
\(f'(x) = 18x^{2}(3x + 2)^{2},\ x\in \mathbb{R}\)
\(f'(x) = 108x^{2},\ x\in \mathbb{R}\)
9000064101
Level:
B
Find the slope of the tangent to the graph of
\(f(x) = x^{2} + 3x - 2\) at the
point \([1;2]\).
\(-\frac{1}
{5}\)
\(5\)
\(- 5\)
\(\frac{1}
{5}\)
9000063410
Level:
B
Solve the following equation.
\[
x + \frac{x}
{3} + \frac{x}
{9} + \frac{x}
{27}+\cdots = 18
\]
\(x = 12\)
\(x = 6\)
\(x = 18\)
\(x = 24\)