Asymptotes: Why to find oblique asymptotes, do you equate the two leading coeffficients to 0.

Question

I am looking at a technique to find asymptotes for a polynomial. I follow the steps, apart from where I have highlighted, surely an-1 can be any number and substituting u=0 into the equation gives an=0?

Answer 1

This is not a formal procedure, but it works.

You have a rational function $f(x)=\frac{P(x)}{Q(x)}$.

The equation of asymptote is $y=mx+c$

Then $$m=\lim_{x\to \infty}f’(x)$$ and $$\lim_{x\to\infty}f(x)-mx=c$$