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Math Help - Real Analysis: Limit

  1. #1
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    Real Analysis: Limit

    Here is the question:



    How do I go about proving this?

    Thank you!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Phyxius117 View Post
    Here is the question:



    How do I go about proving this?

    Thank you!
    Use the squeeze theorem and note that \displaystyle -1 \le \sin \left(\frac{1}{x}\right) < 1 for all x.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by TheEmptySet View Post
    Use the squeeze theorem and note that \displaystyle -1 \le \sin \left(\frac{1}{x}\right) \le 1 for all x.
    ...for all x \text{ such that }\displaystyle x \ne 0.

    Luckily, the limit doesn't care about being at 0, just getting arbitrarily close to it.
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