# How do you find the limit of  [ ( t^2 + 2) / (t^3 + t^2 -1) ] as x approaches negative infinity?

Jul 1, 2016

Limit is 0.

#### Explanation:

Assuming you mean the limit as t approaches negative infinity.

$\frac{{t}^{2} + 2}{{t}^{3} + {t}^{2} - 1}$

Divide through by highest power of 't' (in this case, ${t}^{3}$)

$\frac{\frac{1}{t} + \frac{2}{t} ^ 3}{1 + \frac{1}{t} - \frac{1}{t} ^ 3}$

${\lim}_{t \to - \infty} \frac{\frac{1}{t} + \frac{2}{t} ^ 3}{1 + \frac{1}{t} - \frac{1}{t} ^ 3} = \frac{0 + 0}{1 + 0 + 0} = 0$