New guy asking about Asymptotes of f(x)= x(lnx)

[LearninDaMath]

Hi, new to the forum. I've been using answers.yahoo.com for the past couple weeks. It's good, but not the best for asking follow-on questions to your topic and stuff. I googled "math help" and "math forum" and this site was the sixth link under the search term "math forum." I recognized this site right away because I've come across it recently when trying to understand some calc concepts. Glad to have found and joined this site.


So, I'm hoping someone could show how to algebraically find the vertical and horizontal asymptotes of
f(x) = x(lnx).



P.S. this is just part of a slightly more involved calc problem. The actual problem also asks for the x and y intercepts, max's and mins, and inflection points. But the part of the problem I am stuck on is where it asks to find the vertical and horizontal asymptotes.

 

[JJacquelin]

I'm hoping someone could show how to algebraically find the vertical and horizontal asymptotes of
f(x) = x(lnx).

There is no vertical nor horizontal asymptotes. In fact no asymptote at all.

 

[chiro]

Hey LearninDaMath and welcome to the forums.

In terms of asymptotes, you either have the derivative go to zero or to infinity and more importantly stay that way (for the case when the derivative is zero).

Building on what JJacquelin has said, can you prove that your function does not have the above property?

 

[LearninDaMath]

Thanks. I got some additional information on this problem today. I'll provide an update on the specifics soon. It has to do with taking the limits as x approaches infinity for finding the horizontal asymptote (in which there is no horizontal asymptote like you said) and taking the limit as x approaches 0 for finding the vertical asymptote (in which there is none like you also said).