# Math Help - Showing that a limit exists

1. ## Showing that a limit exists

How would you show that for every $x \in \mathbb{R}$, the limit

$\lim_{m\to \infty} (cos(x))^{2m}$

exists?

2. Originally Posted by FGT12
How would show that for ever $x \in \mathbb{R}$, the limit $\lim_{m\to \infty} (cos(x))^{2m}$
What is the question here?

3. Ive changed it

4. Use the following facts:

(1) $-1\leq \cos x\leq 1$ for all $x$
(2) If $-1, then $-1
(3) As $n$ goes to infinity, $x^n$ goes to 0 if $-1

Now see if you can put the argument together.

5. Actually if $\displaystyle - 1 \leq x \leq 1$ then $\displaystyle 0 \leq x^2 \leq 1$.

6. Thanks Prove It.

Although technically everything I've written is true and is sufficient to finish the argument