Granica ciągu (n-n^2)/(5+n)

[supergolonka]

Oblicz granicę: \(\Limn\frac{n-n^2}{5+n}\).

[supergolonka]

Liczymy \[\Limn\frac{n-n^2}{5+n}=\Limn\frac{n-n^2}{5+n}\cdot \frac{\frac{1}{n}}{\frac{1}{n}}=\Limn\frac{1-n}{\frac{5}{n}+1}=\frac{1-\infty}{0+1}=-\infty.\]

Odpowiedź: \(-\infty\)

[supergolonka]

Oblicz granicę: \(\Limn\frac{3n+n^2}{3-n}\).

[supergolonka]

Liczymy \[\Limn\frac{3n+n^2}{3-n}=\Limn\frac{3n+n^2}{3-n}\cdot \frac{\frac{1}{n}}{\frac{1}{n}}=\Limn\frac{3+n}{\frac{3}{n}-1}=\frac{3+\infty}{0-1}=-\infty.\]

Odpowiedź: \(-\infty\)