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Math Help - Epsilon Delta Limit Proof sinxcos(1/x)

  1. #1
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    Epsilon Delta Limit Proof sinxcos(1/x)

    I'm completely stuck on the limit of sinxcos(1/x) as x goes to 0.

    If you are allowed to take the arcsin of epsilon, then I should be fine, but I have a feeling you aren't allowed to do that. Any hints?
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  2. #2
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    Re: Epsilon Delta Limit Proof sinxcos(1/x)

    Quote Originally Posted by jsmith90210 View Post
    I'm completely stuck on the limit of sinxcos(1/x) as x goes to 0.
    Surely you can see that \left| {\sin (x)\cos \left( {\frac{1}{x}} \right)} \right| \le \left| {\sin (x)} \right|.
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  3. #3
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    Re: Epsilon Delta Limit Proof sinxcos(1/x)

    yes, I can see that, but then I have abs(sinx)<epsilon, i need to get from there to abs(x)<some variation of epsilon and I don't know how to do that
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    Re: Epsilon Delta Limit Proof sinxcos(1/x)

    Quote Originally Posted by jsmith90210 View Post
    yes, I can see that, but then I have abs(sinx)<epsilon, i need to get from there to abs(x)<some variation of epsilon and I don't know how to do that
    Do you know that |\sin(x)|\le |x|~?
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