1003035901
Level:
A
Find the limit \( \lim\limits_{n\rightarrow\infty}\left(4+\frac3{2n-1}\right) \).
\( 4 \)
\( \frac32 \)
\( \infty \)
\( 0 \)
\( \frac{11}2 \)
Limit of a sequence
1003035903
Level:
A
Find the limit \( \lim\limits_{n\rightarrow\infty}\left(5n^2+2n-1\right) \).
\( \infty \)
\( 5 \)
\( 0 \)
\( 2 \)
\( -1 \)
1003035904
Level:
A
Find the limit \( \lim\limits_{n\rightarrow\infty}\left(\frac{2n-2}{n+1}\cdot\frac{5n+3}{n-4}\right) \).
\( 10 \)
\( \infty \)
\( 0 \)
\( 7 \)
\( -6 \)
1003035905
Level:
A
Find the limit \( \lim\limits_{n\rightarrow\infty} \left( \frac{2n-2}{n+1}+\frac{5n+3}{n-4} \right) \).
\( 7 \)
\( \infty \)
\( 0 \)
\( 10 \)
\( -6 \)
1003035906
Level:
A
Find the limit \( \lim\limits_{n\rightarrow\infty}\left( \frac4{n^3} +2+\frac{3n^2+5}{1-n^2}\right) \).
\( -1 \)
\( 0 \)
\( \infty \)
\( 9 \)
\( -\frac13 \)
1003047301
Level:
A
Which of the following expressions describes the correct calculation of the limit?
\[ L=\lim\limits_{n\to\infty}\frac{n^3+2n-3}{2n^3+5}\]
\( L=\lim\limits_{n\to\infty}\frac{1+\frac2{n^2}-\frac3{n^3}}{2+\frac{5}{n^3}}= \frac12 \)
\( L=\frac{\infty^3+2\cdot\infty-3}{2\cdot\infty^3+5}=\infty \)
\( L=\frac{\infty^3+2\cdot\infty-3}{2\cdot\infty^3+5}=0 \)
\( L=\lim\limits_{n\to\infty}\frac{n\left(n^2+2\right)-3}{2n^3+5}= -\frac35 \)
\( L=\lim\limits_{n\to\infty}\frac{\left(n^2+3\right)(n-1)}{2\left(n^3+\frac52\right)}= 0 \)
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 \( n^5 \).
1003047303
Level:
A
Find the limit.
\[ \lim_{n\to\infty}\frac{-3n^2+n-1}{9n^5-3n^2+3} \]
\( 0 \)
\( -\frac13 \)
\( \infty \)
\( -\infty \)
\( \frac13 \)
1003047304
Level:
A
Find the limit.
\[ \lim\limits_{n\to\infty}\frac{-n^2-3}{7n} \]
\( -\infty \)
\( 0 \)
\( \infty \)
\( -\frac37 \)
\( 1 \)
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.