Příklad 2.4

Spočtěte limitu posloupnosti \(\large\lim_{n\to\infty}\frac{1-3n}{7n-n^2}\)

$$\Large \begin{aligned}

& \lim_{n\to\infty}\frac{1-3n}{7n-n^2} \

=& \lim_{n\to\infty}\frac{n\cdot\left(\frac{1}{n}-3\right)}{n^2\cdot\left(\frac{7}{n}-1\right)} \

=& \lim_{n\to\infty}\frac{\cancel{n}^1\cdot\left(\cancel{\frac{1}{n}}^0-3\right)}{\cancel{n^2}^n\cdot\left(\cancel{\frac{7}{n}}^0-1\right)} \

=& \lim_{n\to\infty}\frac{-3}{-n} \ =& \lim_{n\to\infty}\frac{3}{n} \ =& \boxed{\infty} \end{aligned} $$