Limits Involving Infinity

Question

Evaluate 

Options:

1. ∞
2. -∞
3. 0
4. 4/9

Answer 1

Based on the fact that the first terms in the numerator and denominator are x³/x², this tells us there is a slant asymptote because the exponent in the numerator is higher than the exponent in the denominator. So the limit is going to either be ∞ or -∞. A normal parent function in this form would be ∞. The -9 in the denominator tells me there is a reflection on the x axis so the solution would be 2. -∞

(This can also be confirmed by looking at the graph)