# How do you find lim cos(1/t) as t->oo?

Dec 7, 2017

It is one.

#### Explanation:

Logically speaking, as $t \rightarrow \infty$, it follows that $\frac{1}{t} \rightarrow 0$.

Since $\cos 0 = 1$, it follows that ${\lim}_{t \rightarrow 0} \cos \left(\frac{1}{t}\right) = 1$.

Dec 7, 2017

${\lim}_{t \rightarrow \infty} \cos \left(\frac{1}{t}\right) = 1$

#### Explanation:

We have:

${\lim}_{t \rightarrow \infty} \cos \left(\frac{1}{t}\right) = \cos \left({\lim}_{t \rightarrow \infty} \frac{1}{t}\right)$
$\text{ } = \cos 0$
$\text{ } = 1$

We can see that the graph of $y = \cos \left(\frac{1}{x}\right)$ rapidly approaches $y = 1$ even for relatively small $x$:
graph{cos(1/x) [-6, 6, -2, 2]}