What is the limit as x approaches infinity of sin(x)?

1 Answer

As x approaches infinity, the y-value oscillates between 1 and -1; so this limit does not exist.

Thus, the answer is it DNE (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 the limit does not exist.

Example:

  • lim_(x->oo)sinx=DNE

  • lim_(x->oo)(sinx)/(x)=0 (Squeeze Theorum)

This is the same question as below:

How do you show the limit does not exist lim_(x->oo)sin(x) ?