# How do you find lim (5t+2)/(t^2-6t+1) as t->oo?

Jan 28, 2017

$0$

#### Explanation:

Divide terms on numerator/denominator by the highest power of t, that is ${t}^{2}$

$\Rightarrow {\lim}_{x \to \infty} \left(\frac{\frac{5 t}{t} ^ 2 + \frac{2}{t} ^ 2}{{t}^{2} / {t}^{2} - \frac{6 t}{t} ^ 2 + \frac{1}{t} ^ 2}\right)$

$= {\lim}_{x \to \infty} \left(\frac{\frac{5}{t} + \frac{2}{t} ^ 2}{1 - \frac{6}{t} + \frac{1}{t} ^ 2}\right)$

$= \frac{0 + 0}{1 - 0 + 0} = 0$