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Calculadora de asíntotas
Halla las asíntotas paso a paso
La calculadora intentará hallar las asíntotas verticales, horizontales y oblicuas de la función, mostrando los pasos.
Solution
Your input: find the vertical, horizontal and slant asymptotes of the function $$$f(x)=x \ln{\left(x \right)}$$$
Vertical Asymptotes
Can't find 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:
$$$\lim_{x \to \infty}\left(x \ln{\left(x \right)}\right)=\infty$$$ (for steps, see limit calculator).
$$$\lim_{x \to -\infty}\left(x \ln{\left(x \right)}\right)=-\infty$$$ (for steps, see limit calculator).
Thus, there are no horizontal asymptotes.
Slant Asymptotes
Line $$$y=mx+b$$$ is a slant asymptote of the function $$$y=f{\left(x \right)}$$$, if either $$$m=\lim_{x \to \infty}\left(\frac{f{\left(x \right)}}{x}\right)=L$$$ or $$$m=\lim_{x \to -\infty}\left(\frac{f{\left(x \right)}}{x}\right)=L$$$, and $$$L$$$ is finite and nonzero.
Calculate the first limit:
$$$\lim_{x \to \infty} \ln{\left(x \right)}=\infty$$$ (for steps, see limit calculator).
Since the value of the limit is infinite, then there is no slant asymptote in the direction of infinity.
Calculate the second limit:
$$$\lim_{x \to -\infty} \ln{\left(x \right)}=\infty$$$ (for steps, see limit calculator).
Since the value of the limit is infinite, then there is no slant asymptote in the direction of infinity.
Thus, this function doesn't have a slant asymptote.
Answer
Can't find vertical asymptotes.
No horizontal asymptotes.
No slant asymptotes.