1003047310
Level:
A
Find the limit.
\[ \lim\limits_{n\to\infty}\frac{-4n+5}{2n+2} \]
\( -2 \)
\( 0 \)
\( \infty \)
\( -\infty \)
\( \frac52 \)
Limit of a sequence
1003047309
Level:
A
The sequence
\[ \left(\frac{3n^5+2n^3+1}{n^3+3}\right)_{n=1}^{\infty} \]
is divergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=\infty \).
is convergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=0 \).
is convergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=3 \).
is divergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=-\infty \).
has no limit.
1003047308
Level:
A
Choose the best first step to take in order to evaluate the limit of the following sequence.
\[ \left(\frac{3n^2-2n+4}{8n^2+13n+2}\right)_{n=1}^{\infty} \]
We divide the numerator and the denominator by \( n^2 \).
We divide the numerator and the denominator by \( n \).
We substitute \( n=\infty \).
We factor out \( n \) in the numerator and in the denominator separately.
We factor out \( 8 \) in the numerator and in the denominator separately.
1003047307
Level:
A
Find the limit.
\[ \lim\limits_{n\to\infty}\frac{4n^2+n-2}{-5n^2-3n} \]
\( -\frac45 \)
\( 0 \)
\( \infty \)
\( -\infty \)
\( \frac45 \)
1003047306
Level:
A
Which of the following expressions describes the correct calculation of the limit?
\[ L=\lim\limits_{n\to\infty}\frac{7n^4+6n^3-5n^2}{8n^5-7n^4+6} \]
\( L=\lim\limits_{n\to\infty}\frac{\frac7n+\frac6{n^2}-\frac5{n^3}}{8-\frac7n+\frac6{n^5}}=0 \)
\( L=\lim\limits_{n\to\infty}\frac{7+\frac6n-\frac5{n^2}}{8n-7+\frac6{n^4} }=-1 \)
\( L=\lim\limits_{n\to\infty}\frac{7+6-5n^2}{8n-7n+6}=-\infty \)
\( L=\lim\limits_{n\to\infty}\frac{7+\frac6n-\frac5{n^2}}{8-\frac7n+\frac6{n^5}}=\frac78 \)
\( L=\lim\limits_{n\to\infty}\frac{\frac7n+\frac6{n^2}-\frac5{n^3}}{8n-7+\frac6{n^4}}=0 \)
1003047305
Level:
A
The sequence
\[ \left(\frac{12n^3+5n+1}{2n^3-6}\right)_{n=1}^{\infty} \]
is convergent and \( \lim\limits_{n\to\infty}\frac{12n^3+5n+1}{2n^3-6}=6 \).
is convergent and \( \lim\limits_{n\to\infty}\frac{12n^3+5n+1}{2n^3-6}=0 \).
is convergent and \( \lim\limits_{n\to\infty}\frac{12n^3+5n+1}{2n^3-6}=12 \).
is divergent and \( \lim\limits_{n\to\infty}\frac{12n^3+5n+1}{2n^3-6}=\infty \).
has no limit.
1003047304
Level:
A
Find the limit.
\[ \lim\limits_{n\to\infty}\frac{-n^2-3}{7n} \]
\( -\infty \)
\( 0 \)
\( \infty \)
\( -\frac37 \)
\( 1 \)
1003047303
Level:
A
Find the limit.
\[ \lim_{n\to\infty}\frac{-3n^2+n-1}{9n^5-3n^2+3} \]
\( 0 \)
\( -\frac13 \)
\( \infty \)
\( -\infty \)
\( \frac13 \)
1003047302
Level:
A
Choose the best first step to take in order to evaluate the limit of the following sequence.
\[ \left( \frac{4n^5+n^4-n^3+2}{7n^4-2n^2+7n} \right)^{\infty}_{n=1} \]
We factor out \( n^4 \) in the numerator and in the denominator separately.
We factor out \( n^5 \) in the numerator and in the denominator separately.
We factorize a polynomial in the denominator.
We divide the denominator by \( n^4 \).
We divide the numerator by \( n^5 \).
1003047301
Level:
A
Which of the following expressions describes the correct calculation of the limit?
\[ L=\lim\limits_{n\to\infty}\frac{n^3+2n-3}{2n^3+5}\]
\( L=\lim\limits_{n\to\infty}\frac{1+\frac2{n^2}-\frac3{n^3}}{2+\frac{5}{n^3}}= \frac12 \)
\( L=\frac{\infty^3+2\cdot\infty-3}{2\cdot\infty^3+5}=\infty \)
\( L=\frac{\infty^3+2\cdot\infty-3}{2\cdot\infty^3+5}=0 \)
\( L=\lim\limits_{n\to\infty}\frac{n\left(n^2+2\right)-3}{2n^3+5}= -\frac35 \)
\( L=\lim\limits_{n\to\infty}\frac{\left(n^2+3\right)(n-1)}{2\left(n^3+\frac52\right)}= 0 \)