# Math Help - Real Analysis: Limit

1. ## Real Analysis: Limit

Here is the question:

How do I go about proving this?

Thank you!

2. Originally Posted by Phyxius117
Here is the question:

How do I go about proving this?

Thank you!
Use the squeeze theorem and note that $\displaystyle -1 \le \sin \left(\frac{1}{x}\right) < 1$ for all x.

3. Originally Posted by TheEmptySet
Use the squeeze theorem and note that $\displaystyle -1 \le \sin \left(\frac{1}{x}\right) \le 1$ for all x.
...for all $x \text{ such that }\displaystyle x \ne 0$.

Luckily, the limit doesn't care about being at 0, just getting arbitrarily close to it.