Question

Atente-se ao gráfico:

A) 0
B) 1
C) 2
D) + infinito
E) – infinito

Answer 1

$\underset{x \to \infty}{\mathrm{\ell im}}\;\dfrac{2x^{4}+2x-5}{4x^{3}+x^{2}+4x-3}\\ \\ =\underset{x \to \infty}{\mathrm{\ell im}}\;\dfrac{x^{4}\left(2+\frac{2x}{x^{4}}-\frac{5}{x^{4}} \right )}{x^{3}\left(4+\frac{x^{2}}{x^{3}}+\frac{4x}{x^{3}}-\frac{3}{x^{3}} \right )}\\ \\ =\underset{x \to \infty}{\mathrm{\ell im}}\;\dfrac{x^{4}\left(2+\frac{2}{x^{3}}-\frac{5}{x^{4}} \right )}{x^{3}\left(4+\frac{1}{x}+\frac{4}{x^{2}}-\frac{3}{x^{3}} \right )}\\ \\ =\underset{x \to \infty}{\mathrm{\ell im}}\;x\cdot \dfrac{2+\frac{2}{x^{3}}-\frac{5}{x^{4}}}{4+\frac{1}{x}+\frac{4}{x^{2}}-\frac{3}{x^{3}}}\\ \\ =\underset{x \to \infty}{\mathrm{\ell im}}\;x\cdot \dfrac{2}{4}\\ \\ =+\infty\\ \\ \\ \boxed{\underset{x \to \infty}{\mathrm{\ell im}}\;\dfrac{2x^{4}+2x-5}{4x^{3}+x^{2}+4x-3}=+\infty}$