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Math Help - Showing that a limit exists

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by FGT12 View Post
    How would show that for ever x \in \mathbb{R}, the limit \lim_{m\to \infty} (cos(x))^{2m}
    What is the question here?
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  3. #3
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    Ive changed it
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  4. #4
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    Use the following facts:

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

    Now see if you can put the argument together.
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  5. #5
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    Actually if \displaystyle - 1 \leq x \leq 1 then \displaystyle 0 \leq x^2 \leq 1.
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  6. #6
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    Thanks Prove It.

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