One of the more ingenious methods of evaluating limits is using the Sandwich Theorem.
One of the most famous limits is evaluated this way: .
This requires using some knowledge of the unit circle.
The red length is , the green length is and the purple length is .
Notice that the area of the sector is a little larger than that of the smaller triangle, and a little smaller than that of the larger triangle. As you make , the three areas will end up becoming equal.
, and since
It should be clear after being sandwiched that .
[Of course, to be pedantic, this only evaluates the right hand limit (i.e. making from the first quadrant where ), but the left hand limit is evaluated in a near identical manner.]