Details

The sine function is very important in mathematics and physics. The sine function can also serve as a great example to demonstrate the - definition of the limit of a function.

Recall that a function has limit at provided that for every , there is a such that whenever . This gives rise to the concept of an box (or window or rectangle).

The vertical sides of the box turn green for an appropriate choice of and are red otherwise. Changing the sine wave's amplitude, frequency, and the value of interest affects the valid choices of . For a valid choice of , the sine wave does not cross over the bottom or the top of the box.