## Thomas' Calculus 13th Edition

Given : $2 |xy| - \dfrac{x^2 y^2}{6} \lt 4-4 \cos \sqrt {|xy|} \lt 2 |xy|$ Re-arrange as: $2 -\dfrac{|xy|}{6}\lt \dfrac{ 4-4 \cos \sqrt {|xy|}}{|xy|} \lt 2$ Since, $\lim\limits_{(x,y) \to (0,0) } (2 -\dfrac{|xy|}{6})=2$ and $\lim\limits_{(x,y) \to (0,0) } 2=2$ This implies that the limit for $\lim\limits_{(x,y) \to (0,0) } (\dfrac{ 4-4 \cos \sqrt {|xy|}}{|xy|} )=2$ by the Sandwich Theorem. So, our answer is Yes.