Why do Pets show a Burst of Energy before Putting them to sleep?

During my interview with Darkness Radio, I was asked "Why do Pets show a Burst of Energy before putting them to sleep?" Dave, the host said that he experienced this with his dogs before they were euthanized.

The answer is that the dog or cat knows you are helping them move out of pain and cross over into a pain free part of life, and they know that you're doing it out of the intense love you share. 

So, although this "burst of energy" at the end causes grief in pet parents, they actually exhibit it because they're happy to cross over, and thankful pet parents love them enough to recognize that.