Question

Calcule o limite da sequência.
Conforme o enunciado da figura

Answer 1

Resposta:

Opção 4.

Resolução:

$\text{lim}\, a_n=\text{lim}\, \dfrac{4n^2-3n+1}{n^2+10n+5}=\text{lim}\, \left[\dfrac{n^2\cdot\left(4-\dfrac{3}{n}+\dfrac{1}{n^2}\right)}{n^2\cdot\left(1+\dfrac{10}{n}+\dfrac{5}{n^2}\right)}\right]=\text{lim}\, \dfrac{4-\dfrac{3}{n}+\dfrac{1}{n^2}}{1+\dfrac{10}{n}+\dfrac{5}{n^2}}\right]=\dfrac{\text{lim}\,\left(4-\dfrac{3}{n}+\dfrac{1}{n^2}\right)}{\text{lim}\,\left(1+\dfrac{10}{n}+\dfrac{5}{n^2}\right)}=\dfrac{4}{1}=4$