Question

Calcule lim x(2x-7 cos x)/ 3x^2 - 5 sen x + 1

Answer 1

$\lim_{x \to \infty} \frac{x(2x-7cosx)}{3x^2-5senx+1} \\ \\ \lim_{x \to \infty} \frac{2x^2-7xcosx}{3x^2-5senx+1} \\ \\ \lim_{x \to \infty} \frac{ \frac{2x^2}{x^2} - \frac{7xcosx}{x^2} }{ \frac{3x^2}{x^2} - \frac{5senx+1}{x^2} } \\ \\ \lim_{x \to \infty} \frac{ 2 - \frac{7cosx}{x} }{ 3 - \frac{5senx+1}{x^2} } \\ \\ \lim_{x \to \infty} \frac{ 2 - \frac{7cos(\infty)}{\infty} }{ 3 - \frac{5sen(\infty+1)}{(\infty)^2} }$

$\lim_{x \to \infty} \frac{ 2 - \frac{7}{\infty} }{ 3 - \frac{5}{(\infty)^2} } \\ \\ \lim_{x \to \infty} \frac{ 2 - 0 }{ 3 -0 } \\ \\ \lim_{x \to \infty} \frac{ 2 }{ 3 }$