# How do you find lim (3x^2+x+2)/(x-4) as x->0 using l'Hospital's Rule or otherwise?

Nov 19, 2017

$- \frac{1}{2}$

#### Explanation:

The initial form is not indeterminate. We cannot use l'Hospiital for this.

${\lim}_{x \rightarrow 0} \left(3 {x}^{2} + x + 2\right) = 2$ and

${\lim}_{x \rightarrow 0} \left(x - 4\right) = - 4$, so

${\lim}_{x \rightarrow 0} \frac{3 {x}^{2} + x + 2}{x - 4} = \frac{2}{- 4} = - \frac{1}{2}$