Question

How do you find `lim sin(1/x)` as `x->0`?

Answer 1

The limit does not exist.

Explanation:

On any interval containing `0`, `sin(1/x)` takes on the values of `1` and `-1` infinitely many times.

Therefore, the values of `sin(1/x)` cannot be approaching one single value.

graph{sin(1/x) [-2.38, 3.094, -1.216, 1.522]}