I'm having some difficulty understanding oblique asymptotes.
Let's have
$$f(x) = 2x^3+3x^2-12x$$
The oblique asymptote appears only when
$$\lim_{x\to \pm \infty} f(x) = \pm \infty$$
So I need to evaluate two limits.
$$\lim_{x\to + \infty} f(x) = +\infty$$
and
$$\lim_{x\to - \infty} f(x) = -\infty$$
Ok good, it seems we got two oblique asymptotes? One to the right and another to the left?
Let's focus on the one to the right. The slope is
$$m = \lim_{x\to +\infty} \frac{f(x)}{x}$$
Evaluating yields that $m = \infty$.
....... this can't be right. An infinite slope would be a straight vertical line.
What am I doing wrong?