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

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Jun 4, 2017

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:

• ${\lim}_{x \to \infty} \sin x = D N E$

• ${\lim}_{x \to \infty} \frac{\sin x}{x} = 0$ (Squeeze Theorum)

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