The discussion revolves around understanding the multivariate limit of the expression Sin(xy)/x as (x,y) approaches (0,y). Participants are exploring the reasoning behind the limit and the separation of variables in the expression.
The discussion is active with participants seeking clarification on the limit and the methods to approach it. Some guidance has been offered regarding the use of L'Hospital's rule and the treatment of variables.
There is an indication that the original poster has referenced a solution but is seeking deeper understanding of the limit process and variable separation.
trap101 said:So I figured out the solution to lim (x,y)-->(0,y) of Sin(xy)/x, but I figured it out by looking at a solution. I wanted to understand though why with respect to the above limit how Sin(xy)/x = y?
How do you separate the xy in the numerator?
Ray Vickson said:Use l'Hospitals's rule, or else look at the behavior of ##\sin \theta## for small ##|\theta|##.
trap101 said:Using L'Hospital's rule, would I essentially be treating "y" as a constant?