Thread: Question that concerns taking the limit of a multivariable function

1. Question that concerns taking the limit of a multivariable function

The problem I am having trouble with looks like:
$\displaystyle \lim(x,y)\rightarrow(0,0)\ \sin(x)/\sin(y)$
(I apologize if this looks confusing. I'm new to using Latex but I think this is understandable. It is the limit as x & y approach the point (0,0) of the function sin(x) divided by sin(y)).

Am I able to perform L'hopital's rule on this function even though the function in the denominator and numerator do not share the same variables?

Thank you for any help!

2. Originally Posted by UCSociallyDead
The problem I am having trouble with looks like:
$\displaystyle \lim(x,y)\rightarrow(0,0)\ \sin(x)/\sin(y)$
(I apologize if this looks confusing. I'm new to using Latex but I think this is understandable. It is the limit as x & y approach the point (0,0) of the function sin(x) divided by sin(y)).

Am I able to perform L'hopital's rule on this function even though the function in the denominator and numerator do not share the same variables?

Thank you for any help!

If the limit exists then it exists no matter how we choose to "go" to zero with (x,y), so: first choose y = x, and then choose y = -x. What did you get? Thus...?

Tonio