Limites t → -∞ e quando t → ∞

[Xico]

Calcule os limites quando t → -∞ e quando t → ∞ da função f(t) = \(\frac{5t + 4 \sqrt{t^{2}-2t-15}}{6t+5}\)

[skaa]

\(lim_{t\rightarrow \infty}\frac{5t+4\sqrt{t^2-2t-15}}{6t+5}=lim_{t\rightarrow \infty}\frac{5t+4\sqrt{t^2(1-\frac{2}{t}-\frac{15}{t^2})}}{6t}=lim_{t\rightarrow \infty}\frac{5t+4\sqrt{t^2}}{6t}=lim_{t\rightarrow \infty}\frac{5t+4|t|}{6t}=lim_{t\rightarrow \infty}\frac{5t+4t}{6t}=\frac{3}{2}\)


\(lim_{t\rightarrow -\infty}\frac{5t+4\sqrt{t^2-2t-15}}{6t+5}=lim_{t\rightarrow -\infty}\frac{5t+4\sqrt{t^2(1-\frac{2}{t}-\frac{15}{t^2})}}{6t}=lim_{t\rightarrow -\infty}\frac{5t+4\sqrt{t^2}}{6t}=lim_{t\rightarrow -\infty}\frac{5t+4|t|}{6t}=lim_{t\rightarrow -\infty}\frac{5t-4t}{6t}=\frac{1}{6}\)