Sandwich Theoerm

This applet illustrates the sandwich theorem ( or Squeeze theorem or Pinching theorem) through a few examples. The theorem is
  • Suppose that for all in some open interval containing , except possibly at itself. Suppose also that
Then By clicking next another example is shown. Some limits are obvious and could be found without the sandwich theorem. The proof that is not included here. Values for all three functions are shown at and can be reduced by clicking "Closer"
Examine the function values as the points approach the limit for each set of functions. Which function limits could be found easily without the sandwich theorem? Why would other function limits be difficult with other methods?