Lim (x,y)->(0,0) (sinx)(e^y - 1)/xy

How would you start this problem?
I don't know if you can switch into polar coordinates given a sinx function and e^y function

It's much simpler than that!
lim((x,y)→(0,0)) (sin x)(e^y - 1) / (xy)
= lim(x,y)→(0,0)) (sin x / x) * (e^y - 1)/y
= lim(x→0) (sin x / x) * lim(y→0) (e^y - 1)/y
= 1 * lim(y→0) (e^y - 0)/1, by L'Hopital's Rule (for second factor)
= 1.

I hope this helps!