The sandwich theorem for functions of two variables states that if g(x, y)≤f(x, y)≤h(x, y) for all (x, y)≠(x0,y0)
in a disk centered at
(x0,y0)
and if g and h have the same finite limit L as
(x, y)→(x0,y0)
then
lim(x, y)→(x0,y0)f(x, y)=L.
Use this result to support your answers to the question. Does knowing that
2|xy|−x2y26<4−4cos|xy|−−−√<2| xy|
2 | x y | - \frac { x ^ { 2 } y ^ { 2 } } { 6 } < 4 - 4 \cos \sqrt { | x y | } < 2 | x y | tell you anything about
lim(x, y)→(0,0)4−4cos|xy|−−−√|xy|?