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Math Help - Help in limits

  1. #1
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    Unhappy Help in limits

    we study limits in calculus so thats why posting here:
    if f(x)=Floor[2012*sin(x)/x]
    What is Limit x->o[f(x)]?


    *Floor function rounds off to least integer. For e.g. Floor[0.99999999]==0.(and not 1)
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  2. #2
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    Re: Help in limits

    Quote Originally Posted by smatik View Post
    we study limits in calculus so thats why posting here:
    if f(x)=Floor[2012*sin(x)/x]
    What is Limit x->o[f(x)]

    What do you think the answer is and why?
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  3. #3
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    Re: Help in limits

    Hint :

    \lim_{x \to 0}\frac{\sin(x)}{x}=1
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  4. #4
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    Re: Help in limits

    The only tricky part is that sin(x)/x is strictly less than 1. Since floor is discontinuous at every integer, you have to be careful. I hope you can now see the answer and a proof if necessary.
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  5. #5
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    Re: Help in limits

    Now i think its 2011 because sinx/x is slightly less than 1(like 0.9999999999999999999999999999999999...) for x->0 but i've written answer 2012 in my notebook.But i dont remember why i wrote that answer.
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  6. #6
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    Re: Help in limits

    Quote Originally Posted by smatik View Post
    Now i think its 2011 because sinx/x is slightly less than 1(like 0.9999999999999999999999999999999999...) for x->0 but i've written answer 2012 in my notebook.But i dont remember why i wrote that answer.
    Well the answer is 2011.
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