This applet illustrates the sandwich theorem ( or Squeeze theorem or Pinching theorem) through a few examples. The theorem is[br][list][br][*]Suppose that [math]g(x) \le f(x) \le h(x)[/math] for all [math]x[/math] in some open interval containing [math]c[/math], except possibly at [math]x=c[/math] itself. Suppose also that [br][math]\lim_{x\to c} {g(x)} =]\lim_{x\to c} {h(x)} = L. [/math][br][/*][/list][br]Then [math]\lim_{x\to c} {f(x)} = L. [/math][br][br]By clicking next another example is shown. Some limits are obvious and could be found without the sandwich theorem. The proof that [math]g(x) \le f(x) \le h(x)[/math] is not included here.[br]Values for all three functions are shown at [math] \mp \Delta[/math] and [math] \Delta[/math] can be reduced by clicking "Closer"

Examine the function values as the points approach the limit for each set of functions.[br][br]Which function limits could be found easily without the sandwich theorem?[br][br]Why would other function limits be difficult with other methods?