9000063405
Level:
A
Evaluate the following infinite sum.
\[
-\frac{2}
{3} + \frac{1}
{6} -\frac{2}
{6} + \frac{1}
{12} - \frac{2}
{12} + \frac{1}
{24}+\cdots
\]
\(- 1\)
\(-\frac{4}
{3}\)
\(\frac{1}
{3}\)
\(\frac{3}
{2}\)
A
9000063601
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\frac{2n + 3}
{3n - 2}
\]
\(\frac{2}
{3}\)
\(-\frac{3}
{2}\)
\(0\)
\(1\)
9000063603
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\frac{2n^{2} + 1}
{3n - 1}
\]
\(\infty \)
\(\frac{3}
{2}\)
\(0\)
\(- 1\)
9000062405
Level:
A
Evaluate the following one-sided limit.
\[
\lim _{x\to 6^{-}}\frac{3x + 2}
{x - 6}
\]
\(-\infty \)
\(1\)
\(+\infty \)
\(0\)
9000062901
Level:
A
Find the sum of the following geometric series.
\[
-\frac{1}
{3} + \frac{1}
{6} - \frac{1}
{12} + \frac{1}
{24}-\cdots
\]
\(-\frac{2}
{9}\)
\(-\frac{2}
{3}\)
\(\frac{2}
{9}\)
\(\infty \)
9000062403
Level:
A
Evaluate the following limit.
\[
\lim _{x\to -1}\frac{x^{2} - 3x - 4}
{x^{2} + 6x + 5}
\]
\(-\frac{5}
{4}\)
\(\frac{4}
{5}\)
\(\frac{5}
{4}\)
\(-\frac{4}
{5}\)
9000062409
Level:
A
Find the first derivative of the function
\(f(x) = x^{2} + x - 6\) at each of the
\(x\)-intercepts.
\(- 5;\ 5\)
\(- 3;\ 7\)
\(- 7;\ 6\)
\(- 9;\ 6\)
9000062401
Level:
A
Find the derivative of \(f(x) = 3x^{4} - 2x^{3} - 3x^{2}\)
at the point \(x_{0} = -1\).
\(- 12\)
\(0\)
\(12\)
\(24\)
9000062402
Level:
A
Find the second derivative of \(f(x) = x^{4} - 3x^{2}\)
at the point \(x_{0} = 1\).
\(6\)
\(- 2\)
\(- 6\)
\(1\)
9000062404
Level:
A
Evaluate the following limit.
\[
\lim _{x\to +\infty } \frac{x^{3} - x + 1}
{1 - x^{2} - x^{3}}
\]
\(- 1\)
\(0.5\)
\(- 0.5\)
\(1\)