Since you purchased WolframAlpha

Can you type

limit sin(x)/x,x->Infinity

into the WolframAlpha expression box, tap the = at the right end of that and then tap the Step-by-step solution button just below that? Does that give you the complete list of steps or just a first line of a hint?

I've learned something about Wolfram Alpha that I didn't know existed.

If I go to Wolfram Alpha and in the text box type

limit calculator

then a different page appears and it asks me to enter the Computational Inputs. I can enter your two variable expression and then tell it that the variable is x and the value to approach is zero. Then I can click

include second limit

and enter the information for y.and then click Compute.

It gives me a result for approaching those limits from a particular direction. And off to the left is a red button labeled Step-by-step solution. When I click that a menu drops down showing me the steps to find that limit.

I had no idea this was hiding inside Wolfram Alpha.

Perhaps this is the way to get it to do multi variable limits and show you the steps.

Can you reproduce all this?

Thank you (and Bill Nelson) for sorting out where this limit calculator can be found and also what it supports for consecutive limits. My small contribution at this point is to note that multivariate limit computations, for the case when such limits exist, are unlikely ever to support a "Show steps" capability. It would be nice to support it in cases where the limit does not exist (e.g. by showing different path-dependent results). It might also be nice to show it for cases where the limit trivially exists (meromorphic function with denominator not vanishing at point of interest). Other cases involve methods and computational machinery that do not lend themselves to showing steps.