1003035903 Level: AFind the limit \( \lim\limits_{n\rightarrow\infty}\left(5n^2+2n-1\right) \).\( \infty \)\( 5 \)\( 0 \)\( 2 \)\( -1 \)
1003035902 Level: BFind the limit \( \lim\limits_{n\rightarrow\infty}(-1)^n\cdot\frac{3n}{4n^2+7} \).\( 0 \)\( \frac34 \)\( -\frac34 \)\( \frac37 \)\( -\infty \)
1003035901 Level: AFind the limit \( \lim\limits_{n\rightarrow\infty}\left(4+\frac3{2n-1}\right) \).\( 4 \)\( \frac32 \)\( \infty \)\( 0 \)\( \frac{11}2 \)
1003047410 Level: BFind the limit \(\lim\limits_{n\rightarrow\infty}\frac{2\cdot3^n+4^n+5}{3\cdot5^n-1} \).\( 0 \)\( \infty \)\( \frac23 \)\( -5 \)\( 4 \)
1003047409 Level: BThe sequence \( \left(\frac{2\cdot3^n+4^n+5}{4\cdot3^n-1}\right)_{n=1}^{\infty} \) is:divergent and \( \lim\limits_{n\rightarrow\infty}\frac{2\cdot3^n+4^n+5}{4\cdot3^n-1}=\infty \)convergent and \( \lim\limits_{n\rightarrow\infty}\frac{2\cdot3^n+4^n+5}{4\cdot3^n-1}=\frac12 \)convergent and \( \lim\limits_{n\rightarrow\infty}\frac{2\cdot3^n+4^n+5}{4\cdot3^n-1}=\frac14 \)convergent and \( \lim\limits_{n\rightarrow\infty}\frac{2\cdot3^n+4^n+5}{4\cdot3^n-1}=0 \)divergent and it does not have an infinite limit
1003047408 Level: BChoose the best first step to simplify and calculate the limit \(\lim\limits_{n\rightarrow\infty}\frac{3^n+4^{n-1}}{3^n+4^{n+1}} \).We divide the numerator and the denominator by \( 4^n \).We divide the numerator and denominator by \( 3^n \).We substitute \(n=\infty \).We take \( 3^n \) outside the brackets in the numerator and the denominator.We take \( 4 \) outside the brackets in the numerator and the denominator.
1003047407 Level: BFind the limit \( \lim\limits_{n\rightarrow\infty}\frac{3^{n+1}+4^{n+1}}{3^{n-1}+4^{n-1}}\).\( 16 \)\( \frac1{16} \)\( 0 \)\( \infty \)\( 1 \)
1003047406 Level: BChoose the correct formula to calculate the limit. \[ L=\lim\limits_{n\rightarrow\infty}\frac{3^{n+1}+4^n}{2^n} \]\( L=\lim\limits_{n\rightarrow\infty}\left(3\cdot\left(\frac32\right)^n+2^n\right)=\infty \)\( L=\lim\limits_{n\rightarrow\infty}\frac{2^n\left(3\cdot\left(\frac32\right)^n+2^n \right)}{2^n}=0 \)\( L=\lim\limits_{n\rightarrow\infty}\frac{3^n \left(3+\left(\frac43\right)^n\right)}{2^n}=0 \)\( L=\lim\limits_{n\rightarrow\infty}\frac{7^{n+1}}{2^n}=\infty \)\( L=\frac{3^{\infty+1}+4^{\infty}}{2^{\infty}} =\frac72 \)
1003047405 Level: BThe sequence \( \left(\frac{3^n-4^{n-1}}{4^n}\right)_{n=1}^{\infty} \) is:convergent and \(\lim\limits_{n\rightarrow\infty}\frac{3^n-4^{n-1}}{4^n}=-\frac14 \)convergent and \(\lim\limits_{n\rightarrow\infty}\frac{3^n-4^{n-1}}{4^n}=\frac14 \)convergent and \(\lim\limits_{n\rightarrow\infty}\frac{3^n-4^{n-1}}{4^n}=-1 \)convergent and \(\lim\limits_{n\rightarrow\infty}\frac{3^n-4^{n-1}}{4^n}=0 \)divergent
1003047404 Level: BFind the limit \( \lim\limits_{n\rightarrow\infty}\frac{5^{n+1}+6^n}{5^n+6^{n+1} } \).\( \frac16 \)\( \frac56 \)\( 1 \)\( 0 \)\( \infty \)