Question

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

Answer 1

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)` ?