# How do you find lim theta costheta as theta->oo?

Mar 7, 2017

DNE

#### Explanation:

${\lim}_{\theta \to \infty} \theta \cos \theta$

We know that: $- 1 \le \cos \theta \le 1$

So:

$- \theta \le \theta \cos \theta \le \theta$

And:

${\lim}_{\theta \to \infty} - \theta \le {\lim}_{\theta \to \infty} \theta \cos \theta \le {\lim}_{\theta \to \infty} \theta$

$\implies - \infty \le {\lim}_{\theta \to \infty} \theta \cos \theta \le \infty$

Maybe it's stating the obvious but because cosine is periodic, there is no limit.