Калькулятор асимптот

Your input: find the vertical, horizontal and slant asymptotes of the function $f(x)=x^{3} - 3 x^{2}$

The line $x=L$ is a vertical asymptote of the function $y=x^{3} - 3 x^{2}$, if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals $0$ or doesn't exist.

So, find the points where the denominator equals $0$ and check them.

As can be seen, there are no such points, so this function doesn't have vertical asymptotes.

Line $y=L$ is a horizontal asymptote of the function $y=f{\left(x \right)}$, if either $\lim_{x \to \infty} f{\left(x \right)}=L$ or $\lim_{x \to -\infty} f{\left(x \right)}=L$, and $L$ is finite.

Calculate the limits:

$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right)=\infty$ (for steps, see limit calculator).

$\lim_{x \to -\infty}\left(x^{3} - 3 x^{2}\right)=-\infty$ (for steps, see limit calculator).

Thus, there are no horizontal asymptotes.

Since the degree of the numerator is not one degree greater than the denominator, then there are no slant asymptotes.

Answer

No vertical asymptotes.

No horizontal asymptotes.

No slant asymptotes.