Question

calcule os limites de:
lim┬(x→+∞)⁡〖(x(2x-7cosx)/(x^2-5senx+1)〗

Answer 1

Resposta:

Explicação passo-a-passo:

$\lim_{n \to \infty}\dfrac{x(2x-7cosx)}{x^{2}-5senx+1}=\\\\\\= \lim_{n \to \infty}\dfrac{x.x(2-\frac{7cosx}{x})}{x^{2}(1-\frac{5senx}{x^{2}}+\frac{1}{x^{2}})}=\\\\\\= \lim_{n \to \infty}\dfrac{x^{2} (2-\frac{7cosx}{x})}{x^{2}(1-\frac{5senx}{x^{2}}+\frac{1}{x^{2}})}=$

$= \lim_{n \to \infty}\dfrac{2-\frac{7cosx}{x}}{1-\frac{5senx}{x^{2}}+\frac{1}{x^{2}}}=\\\\\\\\=\dfrac{2-0}{1-0+0}}}=2$