Sin(1/x)

Definition

The function sin(1/x) is an oscillating function that varies rapidly as x approaches zero. It has infinitely many peaks and valleys, but it never settles on a single value.

Related terms

Asymptote:

A line that the graph of a function approaches but never touches. In the case of sin(1/x), the y-axis serves as an asymptote.

Periodic Function: A function that repeats its values in regular intervals. While sin(1/x) does not have a fixed period, it exhibits periodic behavior as x approaches zero.

Limit:

The value that a function approaches as the input (x) gets arbitrarily close to a certain point or infinity. For sin(1/x), the limit as x approaches zero does not exist because it oscillates indefinitely.