I'm doing a university real-analysis course and just had a question about a limit and the squeeze principle.
Take...
$x_n = \frac{Sin(n)}{n}$
We know...
$\frac{1}{n} \rightarrow 0 $
Squeeze principle says...
$x_n \leq y_n \leq z_n$. Then $\forall n \geq N $
and that $x_n \rightarrow x$ and $z_n \rightarrow x$ then Then $y_n \rightarrow x $ as $n\rightarrow \infty$.
Therefore...
$\frac{-1}{n} \leq \frac{sin(n)}{n} \leq \frac{1}{n}$
Therefore by squeeze princible...
$\frac{sin(n)}{n} \rightarrow 0$
Is this correct?
Thanks!