• LearninDaMath
In summary, the conversation discusses the experience of a new member on a math forum and their specific question about finding the vertical and horizontal asymptotes of a given function. The forum members provide guidance and clarification on the concept of asymptotes and conclude that the given function does not have any asymptotes.
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.

Last edited:
LearninDaMath said:
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.

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?

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).

Welcome to the forum! It's great to have you here. As for your question, finding asymptotes for a function involves looking at the behavior of the function as x approaches certain values. For horizontal asymptotes, we are looking at the behavior as x approaches positive or negative infinity. In this case, since x(lnx) is an increasing function, as x gets larger and larger, the function will also increase without bound. Therefore, there is no horizontal asymptote.

For vertical asymptotes, we are looking at the behavior as x approaches a specific value, in this case, x=0. As x gets closer and closer to 0, the function will approach negative infinity. Therefore, there is a vertical asymptote at x=0.

To find these asymptotes algebraically, we can use the limit definition of an asymptote. For the horizontal asymptote, we would take the limit as x approaches infinity of x(lnx). This limit would evaluate to infinity, confirming that there is no horizontal asymptote.

For the vertical asymptote, we would take the limit as x approaches 0 from the left and right of x(lnx). This limit would evaluate to negative infinity, confirming the presence of a vertical asymptote at x=0.

I hope this helps! If you have any further questions, don't hesitate to ask. And good luck with the rest of your calculus problem!

## What is an asymptote?

An asymptote is a line that a graph approaches but does not intersect. In other words, as the graph gets closer and closer to the line, it never actually touches it.

## How do you find the asymptotes of a function?

To find the asymptotes of a function, you need to first simplify the function as much as possible. Then, check for any restrictions on the variable. Next, set the denominator equal to zero and solve for the variable. Any values that make the denominator equal to zero will be potential vertical asymptotes. Lastly, check for any horizontal asymptotes by evaluating the limit of the function as x approaches positive or negative infinity.

## What is the equation of the asymptote for f(x) = x(lnx)?

The equation of the vertical asymptote for f(x) = x(lnx) is x = 0. This is because when x = 0, the denominator (lnx) becomes undefined and the function approaches infinity. There are no horizontal asymptotes for this function.

## Can a function have more than one asymptote?

Yes, a function can have multiple asymptotes. It can have both vertical and horizontal asymptotes, and there can be more than one of each type. The number of asymptotes a function has depends on the behavior of the function and the restrictions on the variable.

## Why do we study asymptotes?

Studying asymptotes can help us understand the behavior of a function, especially as the input values get very large or very small. It can also help us identify any restrictions on the variable and the domain of the function. Asymptotes are also important in calculus, as they can help us determine the limit of a function as it approaches a certain value.

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