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

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Answer 1 · 2017-12-08T16:08:42

The limit does not exist.

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]}

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