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Math Help - Limits at infinity of Trigonometric Functions

  1. #1
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    Limits at infinity of Trigonometric Functions

    Here are a few limit questions that I cannot figure out.
    1. Lim x--> Infinity Sin(x)
    2. Lim x--> Infinity (Sin(x)-x)
    3. Lim x--> Infinity (x / Sin(x))
    4. Lim x--> Infinity (Sin(x) / x)

    My answers;
    1. Undefined, since Sin(x) varies b/w -1 and 1 and the end behavior is unknown at infinity
    2. Undefined
    3. Undefined
    4. Zero as x approaches infinity 1/x approaches zero.

    Please help without using L'Hopital's Rule as we have not yet studied that in Calculus. Thank you
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  2. #2
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    by "undefined" , I believe you mean that the limits do not exist. if so, I agree with your results.
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    Quote Originally Posted by skeeter View Post
    by "undefined" , I believe you mean that the limits do not exist. if so, I agree with your results.
    Yes, I should have used "does not exit", which I believe is the proper term. Thanks anyways.
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    Quote Originally Posted by skeeter View Post
    by "undefined" , I believe you mean that the limits do not exist. if so, I agree with your results.
    actually lim x--> infinity ( sin(x) - x) is negative infinity. Can be proven using the squeeze theorem.
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  5. #5
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    Quote Originally Posted by bilalsaeedkhan View Post
    actually lim x--> infinity ( sin(x) - x) is negative infinity. Can be proven using the squeeze theorem.
    does a limit exist if it is infinite? if so, then I guess they should start posting these on the Autobahn ...

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