Solution
As x approaches infinity, the y−value oscillates between 1 and −1; so this limit does not exist.
One good rule to have while solving these problems is that generally, if there is no x in the denominator at all, then limit does not exist.
Example:
x→∞
lim
sinx= does not exist
x→∞
lim
x
sinx
=0 (Squeeze Theorem)
This is the same question as below: