Finding a basic limit Determine the following limit
$$\lim_{n\to\infty} \cos{\left(\frac{n}{2^{n}}\right)}$$
I'm not really sure how to start here. We can write this as $$\cos{\left(\lim_{n\to\infty}\frac{n}{2^{n}}\right)}$$ then we must determine $$\lim_{n\to\infty}\frac{n}{2^{n}}$$ evidently this is zero however how would we actually determine this?

The answer is $1$ because:


*

*The function $\cos x$ is continous on $\mathbb{R}$ and at $x = 0$.

*$\displaystyle \lim_{x\to 0} \cos x = \cos 0 = 1$.

*$\displaystyle \lim_{n \to \infty} \dfrac{n}{2^n} = 0$ ( by L'hospitale rule )
