## Encuentra asíntotas paso a paso

La calculadora intentará encontrar las asíntotas verticales, horizontales y oblicuas de la función, mostrando los pasos.

Enter a function: f(x)=

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### Solution

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

### Vertical Asymptotes

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.

### Horizontal 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.

### Slant Asymptotes

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