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).