Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- yuki

x^3 + xy -y^2 = 10.
is there any way to find the vertical asymptote by hand?
I can do it graphically, but it looks like a problem that is solvable by hand.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

Get your **free** account and access **expert** answers to this and **thousands** of other questions

- yuki

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

Do you mean algebraically?

- yuki

exactly

- yuki

I tried implicit differentiation but I couldn't work it out.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- anonymous

You solve for y, then check out what happens as you move through x. You check for where the function collapses.

- anonymous

I assume you're plotting y vs x?

- yuki

by letting
\[-2y^2+xy+(x^3+10) = 0 \]
and solving for y using the quadratic formula
gave me a curve and I was able to figure out the solution,
but if there is any way to do it algebraically it would be great.
I tried to differentiate the explicit function, too
but that took a very long time and I doubt that it is the natural way.

- yuki

woops, I meant -10

- anonymous

Well, you solve for y as per quadratic and then look at the result to see if there are points where parts of the function will be undefined. Let me do the problem.

- yuki

I appreciate it

- anonymous

\[y=\frac{x \pm \sqrt{x^2-4(10-x^3)}}{2}\]will be a function for y for either the positive or negative square root. The only place this should fall apart is for those x's such that the radicand x^2-4(10-x^3), is less than zero.

- anonymous

For x < about 2.07, the function shouldn't exist. Apart from that, but there are no vertical asymptotes...

- yuki

it seems like the problem looks easy but the answer is not.
Thanks for the help though, it feels good to have other people
making same conclusions as me.

- anonymous

So did that help? Was your question answered?

- anonymous

Do you have plotting software?

- yuki

I just graphed it on my graphing calculator TI-86 and
it did all the job I wanted it to do.

- anonymous

http://www.geogebra.org/cms/

- anonymous

It's free ^^

- yuki

Thanks.

Looking for something else?

Not the answer you are looking for? Search for more explanations.