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Math Help - Basic Limits Question

  1. #1
    Junior Member
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    Basic Limits Question

    Hello everyone,

    I found some trouble with the following questions, although they look simple enough, I don't know how to calculate the limits of the 2 functions even though I know the final answer from Wolframalpha.


    How do I solve these?
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  2. #2
    MHF Contributor
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    For the first limit, the numerator approaches zero while the denominator is bounded between 4 and 6. Therefore, the limit is zero.
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  3. #3
    MHF Contributor
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    Hi

    For the first one use -1 \leq \cos \left(\frac{1}{x}\right) \leq 1
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  4. #4
    MHF Contributor
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    For the second one you can multiply the numerator and the denominator by \sqrt{x}+\sqrt{a} and use x^2-a^2 = (x-a)(x+a)
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