Multivariable Limits- Non Origin Ones? I need your help in the following limits:
1) How can I prove the following limit is zero? 
$$ \lim_{(x,y)\to(1,1)} \frac{\tan(y-1)\sin^2(x-y)}{(x-1)^2+(y-1)^2} \ ? $$
2) It seems like the following limit does not exist, but I don't know how to prove it rigorously:
$$\lim _{(x,y)\to(1,1)} \frac{18(y-1)^4(x-1)^2 + 5(x-y)^2(y-1)^4 } {28(x-1)^6+y(y-1)^6} $$ 
Thanks in advance

There is nothing special about limits at the origin or any other point.  You could define $z=x-1, w=y-1$ and your first becomes $\lim_{(1,1)} \frac{\tan(y-1)\sin^2(x-y)}{(x-1)^2+(y-1)^2}=\lim_{(0,0)} \frac{\tan(w)\sin^2(z-w)}{z^2+w^2}$  Then you can use the small angle approximation to get $\lim_{(0,0)} \frac{w(z-w)^2}{z^2+w^2}$  Now if $w,z$ are both small you have three small factors in the numerator and only two in the denominator.
For 2, what happens if you approach $(1,1)$ along $x=y$?
