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The Squeeze Theorem

Consider the green function g in the applet below. Note how it seems that the graph of function g always stays in between functions f and h. Drag the BIG GREEN POINT as close as possible to the origin. Observe the y-coordinates of the 3 points as you do. Given this information, what would you say the limit as x ==> 0 of g(x) is, given this information? Does this limit even exist? (After all, we clearly know that function g is NOT DEFINED at x = 0). If so, how could you algebraically prove it? (Feel free to zoom in if you'd like).