[tex]\lim_{x \to \infty} \frac{4-x^2}{3-x^2} = \lim_{x \to \infty} (\frac{\infty}{\infty} )=\\\\=\lim_{x \to \infty} \frac{\frac{4}{x^2} -\frac{x^2}{x^2}}{\frac{3}{x^2} -\frac{x^2}{x^2}}=\frac{0-x^2}{0-x^2} = 1[/tex]