Aritmetika limit
Úloha číslo: 2835
Spočítejte následující limity.
Varianta 1
\(\displaystyle \lim_{n\to\infty} \frac{n+1}{n+2}\)
Varianta 2
\(\displaystyle \lim_{n\to\infty} \left(4+\frac1n+\frac3{n^2-2n}\right)\left(5-\frac1{n^2}\right)\)
Varianta 3
\(\displaystyle \lim_{n\to\infty} \frac{3n^2+5n}{-n^2+4n}\)
Varianta 4
\(\displaystyle \lim_{n\to\infty} \frac{2n^2+n-3}{n^3-1}\)
Varianta 5
\(\displaystyle \lim_{n\to\infty} \frac{2n^3+6n}{n^3-7n+7}\)
Varianta 6
\(\displaystyle \lim_{n\to\infty} \frac{n^3-1}{2n^2+n-3}\)
Varianta 7
\(\displaystyle \lim_{n\to\infty} \frac{\sqrt n}{n^3+1}\)
Varianta 8
\(\displaystyle \lim_{n\to\infty} \frac{(2n-3)^{20}(3n+2)^{30}}{(2n+1)^{50}}\)
Varianta 9
\(\displaystyle \lim_{n\to\infty} \frac{3^n+5^n+10^n}{-2^{n+1}+5^{n+1}+10^{n+1}}\)