Granica ciągu (3n-5)/(2-8n)

[supergolonka]

Oblicz granicę: \(\Limn\frac{3n-5}{2-8n}\).

[supergolonka]

Liczymy \[\Limn\frac{3n-5}{2-8n}=\Limn\frac{3n-5}{2-8n}\cdot \frac{\frac{1}{n}}{\frac{1}{n}}=\Limn\frac{3-\frac{5}{n}}{\frac{2}{n}-8}=\frac{3-0}{0-8}=-\frac{3}{8}.\]

Odpowiedź: \(-\frac{3}{8}\)

[supergolonka]

Oblicz granicę: \(\Limn\frac{2n-7}{3-5n}\).

[supergolonka]

Liczymy \[\Limn\frac{2n-7}{3-5n}=\Limn\frac{2n-7}{3-5n}\cdot \frac{\frac{1}{n}}{\frac{1}{n}}=\Limn\frac{2-\frac{7}{n}}{\frac{3}{n}-5}=\frac{2-0}{0-5}=-\frac{2}{5}.\]

Odpowiedź: \(-\frac{2}{5}\)