Find the limit, if it exists. Be sure you can explain your answer.

$\displaystyle \lim_{(x, y) \rightarrow (0,0)} \left<3x^{2}-6y^{2}+8e^{x^{2}-y^{2}},\cos\!\left(6xy\right)\right> =$

Use "infinity" for "$\infty$" and "-infinity" for "$-\infty$". Use "DNE" for "Does not exist".