Showing that $\;\lim_{x\to\infty}\left(1-\frac{x}{4}\right)\exp(-x^2+5x-6)=0$

Question

I have been set this problem in a calculus class:

$$f(x) = \left(1-\frac{x}{4}\right)\exp(-x^2+5x-6),$$

show that the following holds:

$$ \lim_{x\to\infty} f(x) =0.$$

Just don't really know where to start with this - I don't think it's L'Hospital's rule because the bottom of the fraction is not differentiable, have tried differentiating $f(x)$ but not sure where to go from there.

Answer 1

You can write it like $\frac{1-\frac{x}{4}}{e^{x^2-5x+6}}$ then apply L'Hospital's rule.