# How do you find the limit of cos(1/x) as x approaches oo?

Mar 26, 2016

$1$

#### Explanation:

We have

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

If we were to "plug in" $\infty$, we would see that the argument of

$\cos \left(\frac{1}{\infty}\right)$

is approaching

$\cos \left(0\right) = 1$

The trick here is knowing that the limit as $x \rightarrow \infty$ where you have the form

$\frac{\text{constant"/xrarr"constant}}{\infty}$

is going to result in $0$.

We can graph $\cos \left(\frac{1}{x}\right)$ as well -- it should have a horizontal asymptote at $y = 1$.

graph{cos(1/x) [-9.71, 10.29, -3, 3]}
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