# Thread: limit of arcsin/arctan in two variables

1. ## limit of arcsin/arctan in two variables

what is the steps for calculating lim (x,y)->(1,3) [arcsin(3xy-9)/arctan(xy-3)]
i know how to do it in 1 dimension..if let z=xy. can i actually do this?
my solution is 3

actually how to use [tex] code in this forum?
i am new here

thanks!

2. Originally Posted by pokemon1111
what is the steps for calculating lim (x,y)->(1,3) [arcsin(3xy-9)/arctan(xy-3)]
i know how to do it in 1 dimension..if let z=xy. can i actually do this?
my solution is 3

actually how to use [tex] code in this forum?
i am new here

thanks!
Yes. Yes. Click on the relavant link in my signature.

3. Originally Posted by mr fantastic
Yes. Yes. Click on the relavant link in my signature.
New users (anyone with less than 10 posts) can't view links in signatures. (Why? I have no clue.)

The link for the latex tutorial is here: http://www.mathhelpforum.com/math-he...-tutorial.html

4. thanks all
why can i do so? i mean from 2 var->1 variable

5. Since x and y only appear as "xy", you can make that substitution. No matter how (x, y) approaches (1, 3), z= xy approaches 3.

If it had been something like "[arcsin(3xy-9)/arctan(y-3)]" you would not have been able to do that.

6. Originally Posted by HallsofIvy
Since x and y only appear as "xy", you can make that substitution. No matter how (x, y) approaches (1, 3), z= xy approaches 3.

If it had been something like "[arcsin(3xy-9)/arctan(y-3)]" you would not have been able to do that.
what should i write to express this?
just write let z=xy, when (x,y)->(1,3), z->3
then continue like one var?

if something like this, how can i calculate?
thanks~!

7. You would just say something like

Let $z=xy$. So if $(x,y) \to (1,3)$, then $z \to 3$.

Therefore:

$\lim_{(x,y)\to(1,3)} \frac{\arcsin(3xy-9)}{\arctan(xy-3)} = \lim_{z \to 3} \frac{\arcsin(3z-9)}{\arctan(z-3)} = \cdots$

You could continue solving the limit using standard one variable techniques.

8. thank you very much =)